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Question 283256: A mother is twice as old as her daughter now, but 10 years ago, she was 3 times as
old as her daughter. Find their ages at present.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!

Answer by ikleyn(53748)   (Show Source):
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.
A mother is twice as old as her daughter now, but 10 years ago, she was 3 times as
old as her daughter. Find their ages at present.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        In the post by @mananth, the setup equation is written incorrectly.
        His manipulations that follow this incorrect equation, also have many errors,
        although the final answer is correct.

        His solution can not be considered as an etalon, so I came to bring a correct solution.

Let the daughter's age be x
mother's age will be 2x
Ten years ago
daughter's age x-10
Mother's age 2x-10

3(x-10) = 2x-10         <<<---=== This is a CORRECT setup equation

Simplify and find 'x'

3x-30 = 2x-10
3x-2x = 30-10
x = 20 Daughter's age now
Mother's age is 2x = 2*20 = 40 years

Solved correctly.

Question 1002578: Question: Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad, and in 7 years his grandpa will be four times older than Jake. How old is Jake's dad?
I've tried 13*4=52. 52-7=45. 45+3=48. 48/2=24.
I'm not sure what steps I'm missing or what math I'm doing wrong
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad,
and in 7 years his grandpa will be four times older than Jake. How old is Jake's dad?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        As printed in the post, this problem is a lame horse with three legs.
        Why ? - Because no one professional English writer will write "will be four times older than Jake".
        Why ? - Because it is not accepted in English to formulate Math problems using this form.

        So, I will interpret the whole problem in THIS way

Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad, and in 7 years his grandpa will be four times as old as Jake. How old is Jake's dad?

        In this form, the problem is a nice arithmetic problem to solve it MENTALLY by reasoning.

Jack is 13 years old now. In 7 years, Jack will be 13+7 = 20 years old. Hence, in 7 years, Jack's grandpa will be 20*4 = 80 years old. It means that Jack's grandpa is 80-7 = 73 years old now. In 3 years, the grandpa will be 73+3 = 76 years old. Hence, in 3 years, Jack's father will be 76/2 = 38 years old. It means that Jack's father is 38-3 = 35 years old now. ANSWER

Solved in this interpretation.

This problem is a good exercise, since it teaches a student to build a logical chain of steps.

Question 973010: Hi,
I have been trying to solve a word problem, here it is:
Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?

I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation
Thanks
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!

3 years ago today 1 year future Evan y-3 y y+1 Sister 3(y-3)=x-3 x 2(y+1)=x+1

from first equation

from second equation

Subtracting,
, Evan's age today

, his sister's age today

Answer by MathTherapy(10806)   (Show Source):
You can put this solution on YOUR website!

Hi, I have been trying to solve a word problem, here it is: Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now? I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation Thanks ****************************** Let Evan's age be E, and his sister's, S "Three years ago, Evan was one third of his sister's age....." translates to: ------ eq (i) "In a year's time, Evan's age doubled will match his sister's age.....translates to: 2(E + 1) = S + 1 2E + 2 = S + 1 2E + 2 - 1 = S 2E + 1 = S ------ eq (ii) ---- Substituting 2E + 1 for S, in eq (i) 3E - 9 = 2E - 2 ----- Multiplying by LCD, 3 3E - 2E = - 2 + 9 Evan's age, or E = 7

Question 1031850: A man is 4 times old as his daughter was 3 years ago.If their combined ages is 48,how old is the daughter now?

Found 3 solutions by josgarithmetic, n2, ikleyn:
Answer by josgarithmetic(39792)   (Show Source):
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Three years ago Now MAN - 4(d-3) DAUGHTER d-3 d SUM 48

, daughter's age

Answer by n2(79)   (Show Source):
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.
A man is 4 times old as his daughter was 3 years ago.
If their combined ages is 48,how old is the daughter now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the daughter age be x now. 3 years ago her age was (x-3) years. Father's age now is 4(x-3) Our equation is x + 4(x-3) = 48 (the combined age) Simplify and find x x + 4x - 12 = 48 5x = 60 x = 60/5 = 12. ANSWER. The daughter is 12 years old. The father is 4(x-3) = 4*(12-3) = 4*9 = 36 years old. CNECK. Their combined age is 12 + 36 = 48, which is precisely correct.

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
A man is 4 times old as his daughter was 3 years ago.
If their combined ages is 48,how old is the daughter now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is incorrect.
        It is incorrect, since his setup equation is wrong.

        I came to bring a correct solution.

Let the daughter age be x now. 3 years ago her age was (x-3) years. Father's age now is 4(x-3) Our equation is x + 4(x-3) = 48 (the combined age) Simplify and find x x + 4x - 12 = 48 5x = 60 x = 60/5 = 12. ANSWER. The daughter is 12 years old. The father is 4(x-3) = 4*(12-3) = 4*9 = 36 years old. CNECK. Their combined age is 12 + 36 = 48, which is precisely correct.

Solved correctly.

Question 1137386: If Amber's age is fourteen less than three times her age six years ago, she will be sixteen years older than her current age. How old is Amber?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
Current age, n
Age at six years ago, n-6

This part on its own: Amber's age is fourteen less than three times her age six years ago
That would be
and the description an question which came after are nonsense.

Just solving the formed equation

Amber is 16 years old.

Answer by ikleyn(53748)   (Show Source):
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.
If Amber's age is fourteen less than three times her age six years ago,
she will be sixteen years older than her current age. How old is Amber?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        How the problem is formulated/worded/presented in the post, is a blatant nonsense,
        contradicting to human logic.

        The solution by @mananth makes this nonsense in degree 2.

        The solution by Artificial Intelligence (Google overview of Feb.09, 2026) repeats this nonsense.

https://www.google.com/search?q=If+Amber%27s+age+is+fourteen+less+than+three+times+her+age+six+years+ago%2C+she+will+be+sixteen+years+older+than+her+current+age.+How+old+is+Amber%3F&rlz=1C1CHBF_enUS1071US1071&oq=If+Amber%27s+age+is+fourteen+less+than+three+times+her+age+six+years+ago%2C+she+will+be+sixteen+years+older+than+her+current+age.+How+old+is+Amber%3F&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIHCAEQIRiPAjIHCAIQIRiPAtIBCDEwMTNqMGo3qAIIsAIB8QX2P9qU19kUUvEF9j_alNfZFFI&sourceid=chrome&ie=UTF-8

        One condition is just enough to solve the problem completely, and the second condition
        is illogical and is not consistent with the first condition.

        So, the reasonable modification to the problem is THIS:

                If Amber's age is fourteen less than three times her age six years ago, how old is Amber?

        Below is my solution for this modified version.

Let 'x' be the Amber's age now. Then the problem leads to this equation 3*(x-6) - 14 = x. Simplify and find x 3x - 18 - 14 = x, 3x - 32 = x, 3x - x = 32, 2x = 32, x = 32/2 = 16. ANSWER. Amber is 16 years old now.

Solved.

-----------------------

Again, the original formulation of the problem is nonsense.

The solution by @mananth is nonsense in degree 2.

The referred solution by the AI is nonsense, too, repeating the nonsense by @mananth.

A reasonable modification and a solution are presented in my post above.

Always remember that @mananth is not a person. It is a computer code,
which may work correctly or incorrectly, but, in distinction of a normal human,
this code does not know in which mode he currently works - in the right mode or in the wrong mode.
This understanding is outside of the range of its abilities.

            I N T E R E S T I N G

Today, on Feb.09, 2026, I posted this original formulation to other AI site, math-chat.org.

It was smart enough to recognize that the original formulation is/was defective,
and was smart enough to create a reasonable version, exactly as mine.
It also solved completely for this modified formulation, so it acted as a reasonable human and a qualified solver.

Thus I conclude that AI Google Overview is just outdated version of AI.
Why then they keep its outcome in the first position of the Google search output? - It is just out of logic.

All this information was posted to the Google Overview via their feedback system
with the reference to this web-page.

Question 1154747: When Mrs. Lee poured the soup into a pan it was room temperature. if the room was 85*F and the soupès temperature went up by 15.5*F per minute, about how long would it take for the soup to boil
Answer by ikleyn(53748)   (Show Source):
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.
When Mrs. Lee poured the soup into a pan it was room temperature. if the room was 85*F and
the soupès temperature went up by 15.5*F per minute, about how long would it take for the soup to boil
~~~~~~~~~~~~~~~~~~~~~~

In his post, @mananth made a fatal error.

He missed to convert boiling point 100 deg Celsius to degrees Fahrenheit, 212 F,
and got absurdist answer.

So, we should calculate the time as

        t = = 8.194 minutes, or about 8 minutes and 12 seconds.

Solved correctly.

Question 1203623: jack is 7 years older than mia. the sum of there ages is 53.how old is jack.

Answer by ikleyn(53748)   (Show Source):
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.
Jack is 7 years older than Mia. The sum of their ages is 53. How old is Jack.
~~~~~~~~~~~~~~~~~~~~~~~

Again, it is nice problem to solve it MENTALLY in 6 seconds, without using equations.

Indeed, consider/imagine another person Jack' instead of Jack, who (Jack') is 7 years younger than Jack.

Then Jack' and Mia both are of the same age, and the sum of their ages is 53-7 = 46.

Hence, Jack' is 46/2 = 23 years old.

It implies that Jack, the true person, is 23 + 7 = 30 years old.

At this point, the solution is complete.

Question 1204081: the combined age of 2 brothers is 35 years old.7 years ago one brother was twice the age of the other. how many years apart were they born

Answer by ikleyn(53748)   (Show Source):
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.
the combined age of 2 brothers is 35 years old. 7 years ago one brother was twice the age of the other.
how many years apart were they born
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        Nice/ideal problem to solve it MENTALLY, without using equations.

Seven years ago the combined age of the two brothers was 35 - 7 - 7 = 21 years. In addition, we are given that 7 years ago (i.e., at that time), one brother was twice the age of the other. It means (as anyone can get immediately), that 7 years ago the older brother was 14 years old, while the younger brother was 7 years old at that time. Hence, the brothers were born 14-7 = 7 years apart.

Solved.

As clear as 2 - 1 = 1.

Compare with the solution by @mananth.

Question 437671: Cory's age is 20% of her father's age. Forty-two years from now, Cory's age will be two-thirds (2/3) of her father's age. How old are Cory and her father now?
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.

In his post, @manath correctly determined the Cory's age: it is 6 years.

But the age of the father is determined incorrectly by @manath.

The correct answer is: the father is 6*5 = 30 years old.

Question 434074: The sum of the present ages of john and his father is 89 years. After 11 years the age of father will be twice the age of john at that time, find their present ages.
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13327)   (Show Source):
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Given that John's father will be twice as old as John is 11 years from now....

let x = John's age 11 years from now
then 2x = father's age 11 years from now
then x-11 = John's age now
and 2x-11 = father's age now

The sum of their present ages is 89:

(x-11)+(2x-11) = 89
3x-22 = 89
3x = 111
x = 37

John's present age = x-11 = 37-11 = 26
father's present age = 2x-11 = 74-11 = 63

ANSWERS: 26 and 63

---------------------------------------------------------------

I chose to set the problem up in a different way than the other tutors.

Sometimes that can make a big difference in how much work it takes to solve the problem.

It didn't make much difference in this problem....

Answer by josgarithmetic(39792)   (Show Source):
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NOW IN 11 YEARS John 89-m 89-m+11=100-m Father m m+11 SUM 89 89+2*11=111

Description makes that .

John's Father, 63
John, 26

Answer by ikleyn(53748)   (Show Source):
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.
The sum of the present ages of john and his father is 89 years.
After 11 years the age of father will be twice the age of john at that time,
find their present ages.
~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is incorrect.
        His setup and his treatment of equations is erroneous and leads right to abyss.
        I came to make a job accurately and to teach you properly.

john's age =x
father's age = 89-x
..
after 11 years
john's age = x+11
father's age = (89-x)+11 = 100 - x
...
100 - x = 2(x+11)
100 - x = 2x + 22
100 - 22 = 2x + x
78 = 3x
x = 78/3 = 26.

ANSWER. John is 26 years old. The father is 89-26 = 63 years old.

Solved correctly.

Question 426356: A father is nine times the age of his son. In 5 years he will be four times the age of his son. How old are they now?
Found 2 solutions by timofer, ikleyn:
Answer by timofer(155)   (Show Source):
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NOW IN 5 YEARS Father 9x 9x+5 Son x x+5

the son now
Father now,

Answer by ikleyn(53748)   (Show Source):
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.
A father is nine times the age of his son. In 5 years he will be four times the age of his son.
How old are they now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The answer in the post by @mananth is incorrect.
        I came to bring a correct solution (including the answer).

Son's age x Father's age 9x 5 years later Son's age x +5 Father's age 9x+5 In 5 years, the father's age is four times the son age 9x + 5 = 4(x+5) 9x + 5 = 4x + 20 5x = 20-5 5x = 15 /5 x = 3 years Son's age 9x = 27 years Father's age

Solved correctly.

Question 732523: Sally is 10 years older than Tim. In 8 years, the sum of their ages will be 40. Determine how old Sally and Tim are now.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39792)   (Show Source):
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x Sally
y Tim

and .

.
.
.

Answer by ikleyn(53748)   (Show Source):
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.
Sally is 10 years older than Tim. In 8 years, the sum of their ages will be 40.
Determine how old Sally and Tim are now.
~~~~~~~~~~~~~~~~~~~~~~~~

        The solution to this problem in the post by @lynnlo is incorrect.
        I came to bring a correct solution.

Let x be the Tim's age. Then the Sally's age is (x+10) years. In 8 years, Tim's age is (x+8) years, while Sally's age is ((x+10)+8) = (x+18) years. In 8 years, the sum of their ages will be 40 - so we write this equation (x+8) + (x+18) = 40. Simplify and find 'x' 2x + 26 = 40, 2x = 40 - 26 = 14, x = 14/2 = 7. Thus Tim is 7 years old now; Sally is 7+10 = 17 years old now. <<<---=== ANSWER CHECK. (7+8) + (17+8) = 15 + 25 = 40. ! correct !

Solved correctly.

Question 733057: you deposited $45.25 in your checking account. but instead of adding $45.25 to your balace the bank accidentally substracted $45.25. How much money should the bank add to your account to correct the mistake?
Answer by ikleyn(53748)   (Show Source):
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.

The bank should add twice as $45.25, i.e. $90.50 to your account to correct the mistake.

As to me, it should be clear even for a hedgehog.

Question 733673: steven is 6 years older than his sister claudia. The product of the ages of both siblings is 187.Find an equation and calculate the age of steven and claudia
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
steven is 6 years older than his sister claudia. The product of the ages of both siblings
is 187.Find an equation and calculate the age of steven and Claudia
~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the sister's age. Then Steven is (x+6) years old. Write the product equation x*(x+6) = 187. You can reduce it to quadratic equation and solve it via the quadratic formula. But more intelligent way is to notice that in the number 187 the alternate sum of its digits, 1 - 8 + 7 = 0; hence, 187 is divisible by 11. It gives us 11 year for the age of the sister and 11+6 = 17 years for Steven. ANSWER. Claudia is 11 years old. Steven is 17 years old.

Solved.

The solution by @lynnlo is incorrect.

Question 744574: the present age of a father is equal to the sum of ages of his 5 children. 12 years hence the sum of ages of his children will be twice the age of their father. find the present age of the father.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
FIVE children, one father
y, age of father
C, sum of ages of the five children

---------the description

Using second equation

substituting for C,

father's current age

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
the present age of a father is equal to the sum of ages of his 5 children.
12 years hence the sum of ages of his children will be twice the age of their father.
find the present age of the father.
~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the present age of the father. According to the problem, x is equal to the sum of the 5 his children, at the same time. 12 years later, the sum of ages of 5 children will be x+5*12 = x+60 years. At that time the age of the father will be x+12 years. The problem says that 2(x+12) = x + 5*12. To find x, simplify this equation step by step 2x + 24 = x + 60 2x - x = 60 - 24 x = 36. ANSWER. The father is 36 years old now.

Solved.

Question 744595: if father tell his son,i was of your present age where you were born.if the father is 36 now . how old the boy 5 year back.
Answer by ikleyn(53748)   (Show Source):
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.
if father tell his son, I was of your present age where you were born.
if the father is 36 now . how old the boy 5 year back.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

if father tell his son, "I was of your present age where you were born", it means that the father age now is twice the son present age. So, if the father is 36 years old now, then his son is 36/2 = 18 years old. Hence, 5 years back the son was 18-5 = 13 years old. ANSWER

Solved.

Question 794514: Mrs. Lemecha's dad is 5 times as old as he was 40 years ago? how old is Mrs. Lemecha's dad?
Answer by ikleyn(53748)   (Show Source):
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.
Mrs. Lemecha's dad is 5 times as old as he was 40 years ago? how old is Mrs. Lemecha's dad?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        This is a nice problem, but the solution given in the post by @lynnlo is absolutely incorrect.
        I came to bring a correct solution.

Let x be the age of the dad. 40 years ago his age was (x-40) years. Write equation as you read the problem x = 5(x-40) Simplify it step by step and find x x = 5x - 5*40, x = 5x - 200 Collect the terms with 'x' on the right side; move the constant term -200 to the left side changing its sign 200 = 5x - x 200 = 4x x = 200/4 = 50. ANSWER. The dad is 50 years old.

Solved.

This problem teaches to read problem attentively and to make setup accurately and adequately.

Therefore, this problem has great educational/instructional value and teaches to treat Math problems with respect.

Question 674243: Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor, five years after he was married, he had a son who died 4 years before his father at half his father's final age. How long did bob live?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13327)   (Show Source):
You can put this solution on YOUR website!

Solving the problem using all of the given information is a good exercise. However, logical reasoning gives the answer with very little work.

In age problems, all numbers are whole numbers. So in this problem, the age Bob lived to must be a multiple of 6, 12, and 7.

The least common multiple of 6, 12, and 7 is 84; so the age Bob lived to is an integer multiple of 84. Since twice 84 is an unreasonable answer for the age at which Bob died, the answer has to be 84.

ANSWER: 84

Answer by ikleyn(53748)   (Show Source):
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.
Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor,
five years after he was married, he had a son who died 4 years before his father
at half his father's final age. How long did bob live?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Wording in your post is not perfect, but don't despair. There is a classic
well known story problem about Diophantus, famous mathematician of ancient Greece.

Diophantus's youth lasts 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly half as long as his father, and Diophantus died just four years after his son's death. What was his age when he died?

This story problem is precisely what you want to follow literally. So, I will solve it for you.
Again, it is classic of about 2200 years old.

Let x be the Diophantus' age when he died. As we read the problem, we write this equation x = + + + 5 + + 4. To solve, multiply all the terms by the Greatest Common Denominator, which is 12*7 = 84. You will get 84x = 14x + 7x + 12x + 5*84 + 42x + 4*84. Group like terms in right side 84x = (14 + 7 + 12 + 42)x + (5*84 + 4*84), combine like terms 84x = 75x + 756, simplify and find x 84x - 75x = 756, 9x = 756, x = 756/9 = 84. Thus, Diophantus died at the age of 84 years.

Solved.

About Diophantus, read this remarkable Wikipedia article

https://en.wikipedia.org/wiki/Diophantus

https://en.wikipedia.org/wiki/Diophantus

Enjoy ( ! )

Question 626199: my daughter is in year 6 at school and has been given maths homework which i cant help her with i have 2 questions but need to be able to show workings out and be able to understand how we got the answer.
1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit. the sum of the three digits is 4. what number is fatma thinking off
2)who am i, i have 3 digit i can only be divived by myself and one. the sum of my digits is 11 i am under 150
Found 4 solutions by n3, josgarithmetic, n2, ikleyn:
Answer by n3(7)   (Show Source):
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.
1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit.
the sum of the three digits is 4. what number is fatma thinking off
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since the 3-digit number is odd, its last (the ones) digit is 1, or 3, or 5, or 7, or 9. If the last digit is '1', then the hundreds digit is 3 and their sum is just 1 + 3 = 4. So (a) then the tens digit is 0 and (b) the number itself is 301. In addition, it is clear that the restriction " the sum of digits is 4 " makes other options for the last digit IMPOSSIBLE. So, the answer to this problem is .

Solved.

Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
(1)
h, hundreds digit
t, tens digit
u, ones digit

, "three times more than the units digit"

some reworking

The only way this makes any sense is that u=0. This means t=4.
From that, h=0.
010 or 10.
The "number" seems to be a two digit number. Not three-digit.
I must have missed something.

Answer by n2(79)   (Show Source):
You can put this solution on YOUR website!
.
(2) who am i, i have 3 digits. i can only be divided by myself and one. the sum of my digits is 11 and i am under 150.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

They want you find a 3-digit prime number between 100 and 150, with the sum of digits 11. First of all, it is clear that the first digit of this number must be 1. Hence, the sum of two remaining digits must be 10. Next, the last (the ones) digits can not be even number, since, otherwise, the number in this interval is not a prime. Also, it is clear that the last digit can not be 5, since, otherwise, the number is divisible by 5. Taking this in account, we see that the last (= the ones) digit should be 1, or 3, or 7, or 9. If the ones digit is 1, then the tens digit is 10-1 = 9, and the number itself is 191. This does not work, since 191 is greater than 150. If the ones digit is 3, then the tens digit is 10-3 = 7, and the number itself is 173. This does not work, since 173 is greater than 150. If the ones digit is 7, then the tens digit is 10-7 = 3, and the number itself is 137. This works, since 137 is a prime number (it is not divisible by 2, 3, 5, 7, 11, and it is just enough to see that 137 is a prime). If the ones digit is 9, then the tens digit is 10-9 = 1, and the number itself is 119. This does not work, since 119 = 7*17 is not a prime number. Thus, we analyzed all possible cases and by the method of exclusion PROVED that there is one and only one possible answer, which is the number of .

Solved.

--------------------------------

The solution method is a logical analysis in three steps.

First, we filter out many possible numbers based on simple divisibility properties.

Then we analyze the remaining 4 cases and exclude three of them that do not work.

Finally, we check that the remaining number satisfies all the conditions.

This way we find a UNIQUE solution to the problem.

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
(2) who am i, i have 3 digits. i can only be divided by myself and one. the sum of my digits is 11 and i am under 150.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        This problem is nice.
        As it is given, it is clear that the solution should be (a) logical   and (b) not very complicated.
        The logic should be accessible for a young student (a 6th grade ?)

        From this point of view, it is clear that the @Theo solution does not satisfy these criterions.

        So, I will present here another, more adequate solution.

So, they want you find a 3-digit prime number between 100 and 150, with the sum of digits 11. First of all, it is clear that the first digit of this number must be 1. Hence, the sum of two remaining digits must be 10. Next, the last (the ones) digits can not be even number, since, otherwise, the number in this interval is not a prime. Also, it is clear that the last digit can not be 5, since, otherwise, the number is divisible by 5. Taking this in account, we see that the last (= the ones) digit should be 1, or 3, or 7, or 9. If the ones digit is 1, then the tens digit is 10-1 = 9, and the number itself is 191. This does not work, since 191 is greater than 150. If the ones digit is 3, then the tens digit is 10-3 = 7, and the number itself is 173. This does not work, since 173 is greater than 150. If the ones digit is 7, then the tens digit is 10-7 = 3, and the number itself is 137. This works, since 137 is a prime number (it is not divisible by 2, 3, 5, 7, 11, and it is just enough to see that 137 is a prime). If the ones digit is 9, then the tens digit is 10-9 = 1, and the number itself is 119. This does not work, since 119 = 7*17 is not a prime number. Thus, we analyzed all possible cases and by the method of exclusion PROVED that there is one and only one possible answer, which is the number of .

Solved.

--------------------------------

The solution method is a logical analysis in three steps.

First, we filter out many possible numbers based on simple divisibility properties.

Then we analyze the remaining 4 cases and exclude three of them that do not work.

Finally, we check that the remaining number satisfies all the conditions.

This way we found a UNIQUE solution to the problem.

From the point of view of complexity, this solution is ACCESSIBLE for young students of the 6th grade interested in Math.

So, it is correct, clear, accessible, adequate and instructive - all what we do expect from a true Math solution.

Question 630202: May you pls help me with this question
"In 9 years time,the mother will be twice as old as her son,she was 4 times older than her son after 3 years.find their age?
Thank you tutor.
kaaliendjala@gmail.com
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
May you pls help me with this question
"In 9 years time, the mother will be twice as old as her son, she was 4 times older than her son after 3 years. find their age?
Thank you tutor.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This post violates the rules of English grammar in part of sequence of tenses : the words and the times are not consistent.
So, if to read/understand it literally as it is written, it makes no sense and is not an object for discussions.

So, in this form, this written " problem " is nonsense.

There are two ways to react on it :   either throw to a garbage bin - - - or edit it from scratch to make it correctly.

Also, for your information, this form

    "she was 4 times older than her son after 3 years."

is not used in Math problems written in English, since in English, unlike many other languages,
this form creates ambiguity unacceptable in Math problems.

It is why the other tutor obtained absurdist answer in his post.

Question 630681: Can you please help,Von is thrice as old as his brother Jon. Four years ago, he was 4 years less than 5 times Jon�s age at that time. How old are they now?

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
Can you please help,
Von is thrice as old as his brother Jon. Four years ago, he was 4 years less than 5 times Jon's age at that time.
How old are they now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        This problem can be solved in hard way, using two equations and writing many words, as tutor @Theo did in his post.

        It also can be solved in easy way, using one equation and writing only the necessary words, as I present it below.

Let x be the Jon age. Then the Von age is 3x, according to the problem. Four years ago, the Jon's age was x-4. Four years ago, the Von's age was (3x-4). From the problem, we have this equation 3x-4 = 5(x-4) - 4. (Four years ago, Von was 4 years less than 5 times Jon's age at that time). It is an equation to solve. Simplify and find x 3x - 4 = 5x - 20 - 4. Collect the terms with 'x' on the right side; collect the constant terms on the left side -4 + 20 + 4 = 5x - 3x, 20 = 2x x = 20/2 = 10. Thus, Jon is 10 years old; Von is 3*10 = 30 years old. <<<---=== ANSWER

Solved.   The solution is clear, transparent and straightforward, with no excessive words that only distract attention.

Question 503855: How do I set up this problem, there were 1.388 millions childcare workers in 2006. The number of job opportunities in that fieldis expected to grow to 1.636 million by 2016. What is the percent of increase?
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
How do I set up this problem, there were 1.388 millions childcare workers in 2006.
The number of job opportunities in that field is expected to grow to 1.636 million by 2016.
What is the percent of increase?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        Tutor @Theo incorrectly reads the problem and incorrectly treats it.
        His solution is irrelevant, and his answer is incorrect.

They ask about the percentage of change between the new value and the old value. The standard formula for it is new value - old value the percent of change = ------------------------ x 100. old value As we apply it with the numbers, we get the percent of change = = 17.867 (approximately). What you need to know: (a) if not said explicitly, divide by the old value, by default; (b) multiply the ratio by 100 to transform the ratio's value to the percentage value.

Solved.

Question 1210341: 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

Found 3 solutions by greenestamps, ikleyn, josgarithmetic:
Answer by greenestamps(13327)   (Show Source):
You can put this solution on YOUR website!

x = son's age now
5x = man's age now
x+15 = son's age in 15 years
5x+15 = man's age in 15 years

In 15 years the man will be twice as old as his son:

5x+15 = 2(x+15)
5x+15 = 2x+30
3x=15
x=5

ANSWERS:
The son's age now is x = 5
The man's age now is 5x =25

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.

        One and ONLY ONE problem/question per post.

It is the RULE, the POLICY and the REQUIREMENT of this forum.

It is written in this page

https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/

from which you post your problems.

It is assumed that you read these rules before posting.

It is also assumed that you do understand what is written in that page and follow the rules.

        This rule is established for benefits of visitors (to avoid mess in responses).

        Those who violate them, work against their own interests.

Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
Too many asked at once. I will only do #10.

---
10. A man is 5 times as old as his son. In 15 years, he will be twice as old. How old are they now?
---

m, the man's age now
m/5, his son's age now

The second sentence means exactly .
You did not specify without amiguity.

Question 1209904: Simon is one fifth of Danielle's age.
In 6 Years time, Simon will be one third of Danielle's age.
How old is Danielle now?

Found 3 solutions by greenestamps, timofer, josgarithmetic:
Answer by greenestamps(13327)   (Show Source):
You can put this solution on YOUR website!

Simon is one-fifth of Danielle's age -- i.e., Danielle is 5 times as old as Simon:

Let x be Simon's age
Then Danielle's age is 5x.

In 6 years, their ages will be x+6 and 5x+6. At that time, Simon will be one-third as old as Danielle -- i.e., she will be 3 times as old as he is:

Simon's age is x = 6
Danielle's age is 5x = 30

ANSWER: Danielle is 30

Answer by timofer(155)   (Show Source):
You can put this solution on YOUR website!
NO!
Danelle, 30 and Simon, 6.

Solve could be like this.

so Danielle is 30.

Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
If you want to follow exactly the way described, then x for Simon and d for Danielle,

, and solve!

Question 1172092: Mrs. Reyes bought a television set and a DVD player. After paying a 60% down payment on each item, she paid the rest in 12 monthly installments. After half a year, Mrs. Reyes paid 1/4 more for the balance owed for the television set than the DVD player. If she had already paid P2000 more for television set, what was the total amount she would have to pay in installment each month if she only paid a 55% down payment on each item?
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website!
Let's break down this problem step-by-step.
1. Define Variables
Let T be the total price of the television set.
Let D be the total price of the DVD player.
2. Set Up Equations Based on the Given Information
60% Down Payment:
Mrs. Reyes paid 0.6T as a down payment for the TV and 0.6D for the DVD player.
The remaining balance for the TV is 0.4T, and for the DVD player is 0.4D.
12 Monthly Installments:
The monthly installment for the TV is 0.4T / 12, and for the DVD player is 0.4D / 12.
Half a Year (6 Months):
After 6 months, Mrs. Reyes had paid half of the balance: 0.2T for the TV and 0.2D for the DVD player.
1/4 More for TV Balance:
The remaining balance for the TV after 6 months was 1/4 more than the remaining balance for the DVD player:
0.2T = 0.2D + (1/4)(0.2D)
0.2T = 0.2D + 0.05D
0.2T = 0.25D
T = 1.25D
P2000 More for TV:
Mrs. Reyes had already paid P2000 more for the TV:
0.6T + 0.2T = 0.6D + 0.2D + 2000
0.8T = 0.8D + 2000
3. Solve for T and D
Substitute T = 1.25D into the second equation:
0.8(1.25D) = 0.8D + 2000
D = 0.8D + 2000
0.2D = 2000
D = 10000
Substitute D back into T = 1.25D:
T = 1.25(10000)
T = 12500
4. Calculate Monthly Installments with 55% Down Payment
55% Down Payment:
New balance for the TV: 0.45T = 0.45(12500) = 5625
New balance for the DVD player: 0.45D = 0.45(10000) = 4500
Total New Balance:
Total balance = 5625 + 4500 = 10125
Monthly Installment:
Monthly installment = 10125 / 12 = 843.75
Answer
The total amount she would have to pay in installments each month if she only paid a 55% down payment on each item is P843.75.

Question 1177079: Grace is more than 20 years old when her first son was born. Today the sum of their age is no less than 60. Solve using Polya's Method.
Found 2 solutions by ikleyn, timofer:
Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
Grace is more than 20 years old when her first son was born. Today the sum
of their age is no less than 60. Solve using Polya's Method.
~~~~~~~~~~~~~~~~~~~~

This problem does not ask question.

So, it is not a Math problem, at all.

It is a fantasy of a mathematically illiterate person, who, in addition,
write inattentively and does not understand what he writes and for what reason.

The right place for this post is a garbage bin.

Answer by timofer(155)   (Show Source):
You can put this solution on YOUR website!
Along a path to looking for a solution, g for Grace and y for her son, p for how many years from his birth until now

p would be at least 30.

Not finished.
Other methods may be better.