Questions on Word Problems: Age answered by real tutors!

Tutors Answer Your Questions about Age Word Problems (FREE)

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

Found 3 solutions by greenestamps, ikleyn, josgarithmetic:
Answer by greenestamps(13200)   (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(52787)   (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(39617)   (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(13200)   (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(104)   (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(39617)   (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(1959)   (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(52787)   (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(104)   (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.

Question 1177283: 4. An airplane diving at an angle of 40.9º below the horizontal drops a mailbag from an
altitude of 900 m. The bag strikes the ground 5.00 s after its release.
a) What is the speed of the plane?
b) How far does the bag travel horizontally during its fall?
c) What are the horizontal and vertical components of its velocity just before it
strikes the ground?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**Given Information:**
* Angle (θ): 40.9° below the horizontal
* Altitude (y): 900 m
* Time (t): 5.00 s
**a) What is the speed of the plane?**
1. **Vertical Motion:**
* We can use the kinematic equation: y = v₀y * t + (1/2) * g * t²
* Where:
* y = vertical displacement (900 m)
* v₀y = initial vertical velocity
* g = acceleration due to gravity (9.8 m/s²)
* t = time (5.00 s)
2. **Calculate Initial Vertical Velocity (v₀y):**
* 900 = v₀y * 5 + (1/2) * 9.8 * 5²
* 900 = 5v₀y + 4.9 * 25
* 900 = 5v₀y + 122.5
* 777.5 = 5v₀y
* v₀y = 155.5 m/s
3. **Calculate Speed of the Plane (v₀):**
* v₀y = v₀ * sin(θ)
* v₀ = v₀y / sin(θ)
* v₀ = 155.5 / sin(40.9°)
* v₀ = 155.5 / 0.6549
* v₀ ≈ 237.44 m/s
**b) How far does the bag travel horizontally during its fall?**
1. **Calculate Initial Horizontal Velocity (v₀x):**
* v₀x = v₀ * cos(θ)
* v₀x = 237.44 * cos(40.9°)
* v₀x = 237.44 * 0.7558
* v₀x ≈ 179.46 m/s
2. **Calculate Horizontal Distance (x):**
* x = v₀x * t
* x = 179.46 * 5.00
* x ≈ 897.3 m
**c) What are the horizontal and vertical components of its velocity just before it strikes the ground?**
1. **Horizontal Velocity (vx):**
* vx = v₀x (horizontal velocity remains constant)
* vx ≈ 179.46 m/s
2. **Vertical Velocity (vy):**
* vy = v₀y + g * t
* vy = 155.5 + 9.8 * 5
* vy = 155.5 + 49
* vy = 204.5 m/s
**Answers:**
* **a) The speed of the plane is approximately 237.44 m/s.**
* **b) The bag travels approximately 897.3 m horizontally.**
* **c) The horizontal component of the velocity is approximately 179.46 m/s, and the vertical component is 204.5 m/s.**

Question 1209777: 01. Manalo is 28 yrs. older than Velasco. In 6years. Manalo will be three times as old as Velasco. How old is Manalo now?

Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**1. Define Variables**
* Let M be Manalo's current age.
* Let V be Velasco's current age.
**2. Translate the First Sentence into an Equation**
* "Manalo is 28 years older than Velasco": M = V + 28
**3. Translate the Second Sentence into an Equation**
* "In 6 years":
* Manalo's age will be M + 6.
* Velasco's age will be V + 6.
* "Manalo will be three times as old as Velasco": M + 6 = 3(V + 6)
**4. Simplify the Second Equation**
* M + 6 = 3V + 18
* M = 3V + 12
**5. Solve the System of Equations**
We have two equations:
* M = V + 28
* M = 3V + 12
Since both equations equal M, we can set them equal to each other:
* V + 28 = 3V + 12
* 28 - 12 = 3V - V
* 16 = 2V
* V = 8
Now, substitute V = 8 back into the first equation:
* M = 8 + 28
* M = 36
**6. Answer the Question**
We are asked to find Manalo's current age, which is M.
**Therefore, Manalo is 36 years old.**

Question 1209778: Flores is is 13yrs younger than Rivero In 8 yrs. the sum of their age will be 41. How old is Flores?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**1. Define Variables**
* Let F be Flores' current age.
* Let R be Rivero's current age.
**2. Translate the First Sentence into an Equation**
* "Flores is 13 years younger than Rivero": F = R - 13
**3. Translate the Second Sentence into an Equation**
* "In 8 years":
* Flores' age will be F + 8.
* Rivero's age will be R + 8.
* "The sum of their ages will be 41": (F + 8) + (R + 8) = 41
**4. Simplify the Second Equation**
* F + 8 + R + 8 = 41
* F + R + 16 = 41
* F + R = 41 - 16
* F + R = 25
**5. Solve the System of Equations**
We have two equations:
* F = R - 13
* F + R = 25
Substitute the first equation into the second equation:
* (R - 13) + R = 25
* 2R - 13 = 25
* 2R = 25 + 13
* 2R = 38
* R = 19
Now, substitute R = 19 back into the first equation:
* F = 19 - 13
* F = 6
**6. Answer the Question**
We are asked to find Flores' age, which is F.
**Therefore, Flores is 6 years old.**

Question 1209779: The sum of quarter of what Elijah's age was 4 yrs ago and double of what it will be in 2 yrs is 66.
How old is Eliyah?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**1. Define the Variable**
Let E be Elijah's current age.
**2. Translate the Word Problem into an Equation**
* "4 years ago": Elijah's age was E - 4
* "Quarter of what Elijah's age was 4 years ago": (1/4)(E - 4)
* "2 years from now": Elijah's age will be E + 2
* "Double of what it will be in 2 years": 2(E + 2)
* "The sum of quarter of what Elijah's age was 4 years ago and double of what it will be in 2 years is 66": (1/4)(E - 4) + 2(E + 2) = 66
**3. Solve the Equation**
* (1/4)(E - 4) + 2(E + 2) = 66
* (E - 4)/4 + 2E + 4 = 66
* Multiply the entire equation by 4 to eliminate the fraction:
* E - 4 + 8E + 16 = 264
* Combine like terms:
* 9E + 12 = 264
* Subtract 12 from both sides:
* 9E = 252
* Divide both sides by 9:
* E = 28
**4. Check the Answer**
* 4 years ago, Elijah was 28 - 4 = 24. A quarter of that is 24/4 = 6.
* In 2 years, Elijah will be 28 + 2 = 30. Double that is 30 * 2 = 60.
* 6 + 60 = 66. The answer checks.
**Therefore, Elijah is 28 years old.**

Question 1209753: my brother is 7 years younger than me. Twice my age plus 3 times his age is 99.What are our ages?
Plz use the singapore model method. I have the answer but can not understand how to show the working out using the bar model.

Found 4 solutions by josgarithmetic, ikleyn, Edwin McCravy, CPhill:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
The person speaking, w
The brother, w-7
Second sentence, .

--------the person giving the description
--------his brother

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
my brother is 7 years younger than me. Twice my age plus 3 times his age is 99.
What are our ages? Plz use the singapore model method.
I have the answer but can not understand how to show the working out using the bar model.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        This problem can be solved MENTALLY, without using any equations,
        based on common sense ONLY.

Mentally, reduce your age by 7 years, to the age of your brother. Then "twice my age plus 3 times his age" will become 99 - 2*7 = 85. Now this "twice my age plus 3 times his age" is the same as 5 times the brother age. Hence, the brother age is 85/5 = 17 years, and your real age is 7 years more, or 17+7 = 24 years. ANSWER. You are 24 years old. Your brother is 17 years old.

Solved mentally, in extremely simple way.

I believe that this solution is accessible for a 4-th grade student.

Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!

The first sentence is: My brother is 7 years younger than ('my age'). It mentions 'my age' second, so: Let this bar be 'my age': And since the brother BRO is 7 years younger, we use a shorter bar for 'BRO's age'. Now notice that "my age" can be partitioned off into 'bro's age' and 7 more, like this: Now we look at the next sentence: Twice my age plus 3 times his age is 99. So we make 2 long bars for 'my age' and 3 short bars for 'bro's age': Now let's partition off the bars for 'my age' as we did above: Now we count the BRO's and there are 5 of them. We count the 7's and there are 2 of them, so the equation is 5 BRO's + 2 7's = 99 or 5B + 2x7 = 99 5B + 14 = 99 Subtract 14 from both sides: 5B = 85 Divide both sides by 5: B = 17 BRO is 7 years younger, so 'your age' is 17 + 7 or 24. Edwin

Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website!
Let's break this problem down step-by-step:
1. **Define Variables:**
* Let "x" represent your age.
* Let "y" represent your brother's age.
2. **Translate the First Sentence into an Equation:**
* "My brother is 7 years younger than me."
* This translates to: y = x - 7
3. **Translate the Second Sentence into an Equation:**
* "Twice my age plus 3 times his age is 99."
* This translates to: 2x + 3y = 99
4. **Solve the System of Equations:**
* We have two equations:
* y = x - 7
* 2x + 3y = 99
* Substitute the first equation (y = x - 7) into the second equation:
* 2x + 3(x - 7) = 99
* Simplify and solve for x:
* 2x + 3x - 21 = 99
* 5x - 21 = 99
* 5x = 120
* x = 24
5. **Solve for y:**
* Now that you know x = 24, substitute it back into the equation y = x - 7:
* y = 24 - 7
* y = 17
**Answer:**
* Your age is 24 years old.
* Your brother's age is 17 years old.

Question 1209587: When I was 6, I was twice as old as my sister. Now I'm 70. How old is my sister?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
When I was 6, I was twice as old as my sister. Now I'm 70. How old is my sister?
~~~~~~~~~~~~~~~~~~~~~~~~

From the problem, when you were 6 years old, your sister was 3 years old.
So, you are 3 years older than your sister.

Hence, now, when you are 70 years old, your sister is 70-3 = 67 years old.

Solved, answered and explained.

Question 1209586: Lena is twice as old as her sister Mia. Four years ago, the sum of their ages was 24. How old are Lena and Mia now?
Found 2 solutions by josgarithmetic, timofer:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!

Age now 4 years ago Lema 2x 2x-4 Mia x x-4 TOTAL 24

-

-this is about 10 years 8 months.

Lena is 2x so -which is 21 years 4 months.

Answer by timofer(104)   (Show Source):
You can put this solution on YOUR website!
Lena----------------
Mia-----------------

Four years ago -------

, MAYBE

Probably need recheck the original problem.

Question 1192305: On her birthday in 2007, Rachel's age is equal to twice the sum of the digits of the
year in which she was born. How many possible years are there in which she could
have been born?
Found 2 solutions by greenestamps, htmentor:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

First suppose she is very young and was born after 2000.

The year she was born can be represented as 2000+B.
Her age in 2007 was 2007-(2000+B) = 7-B.
The sum of the digits of the year she was born is 2+B.
Her age is twice the sum of the digits:

So one possibility is that she was born in 2001. The sum of the digits of that year is 3, and her age is 2007-2001 = 6.

Now look for possibilities that she was born before 2000.

The year she was born (19AB) can be represented as 1900+10A+B.
Her age in 2007 was 2007-(1900+10A+B) = 107-10A-B.
The sum of the digits of the year she was born is 1+9+A+B = 10+A+B.
Her age is twice the sum of the digits:

A and B are non-negative single-digit integers. There are three solutions, easily found by inspection.

(1) A=7, B=1. She was born in 1971; her age is 2007-1971=36; the sum of the digits of her birth year is 1+9+7+1 = 18.

(2) A=6, B=5. She was born in 1965; her age is 2007-1965=42; the sum of the digits of her birth year is 1+9+6+5 = 21.

(3) A=5, B=9. She was born in 1959; her age is 2007-1959=48; the sum of the digits of her birth year is 1+9+5+9 = 24.

ANSWER: 4 possible years for her birth (2001, 1971, 1965, and 1959)

Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website!
First, let's consider the possibility that Rachel was born in the 2000's. Then we can express the year she was born as 2000 + x. Thus, her age A = 2007 - (2000 + x)
If twice the sum of the digits = her age, we can write A = 2(2 + x).
Thus, we have two equations A = 4 + 2x and A = 7 - x.
Multiplying the 2nd equation by 2, and adding (1) and (2) we get:
3A = 18 -> A = 6.
Now, we consider if Rachel is born in the year 19xy.
Then we can express the year she was born as 1900 + 10x + y, and her age would be:
A = 2007 - (1900 + 10x + y)
And the equation for twice the sum of the digits is:
2(1 + 9 + x + y) = A
Simplifying we have 107 - 10x - y = A and 20 + 2x + 2y = A
The expression for x in terms of A, which we get by multiplying (1) by 2 and adding, is: A = 78 - 6x
Since x can take on the values [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], we have these possible ages: [78, 72, 66, 60, 54, 48, 42, 36, 30, 24].
This gives possible birth years [1929, 1935, 1941, 1947, 1953, 1959, 1965, 1971, 1977, 1983].
Of these, only 1959, 1965 and 1971 have the correct x value.
So, the answer is 1959, 1965, 1971 and 2001.

Question 1209414: Xavier shoots a basketball in which the height, in feet, is modeled by the following equation:
h(t)= −4t2+10t+18
, where t
is time, in seconds.
What is the maximum height of the basketball in feet? Round your answer to the nearest hundredth.

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
Xavier shoots a basketball in which the height, in feet, is modeled by the following equation:
h(t)= −4t2+10t+18
, where t is time, in seconds.
What is the maximum height of the basketball in feet? Round your answer to the nearest hundredth.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As it is written, this formula does not work.

            Introduction written specially for beginners who don't know the subject AT ALL

The formula in your post is written incorrectly.   FATALLY INCORRECTLY, it is what I want to say.

I observed it many times in this forum that the students / (the visitors) write this formula incorrectly.
because they do not understand the meaning of its terms.

So I prepared this text below as a standard introduction to the subject for such students / visitors.

Be calm, you are in good hands, and read my post to the very end.

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

If you have the formula for a height given to you as a function of time in the form h(t) = -at^2 + bt + c, (1) where "a", "b" and "c" are real numbers, a > 0, then in this formula (a) the initial height is equal to the coefficient "c" value; (b) the initial velocity is the coefficient "b" in the formula; (c) the coefficient "a" value is half of the gravity acceleration. For the Earth conditions, the gravity acceleration is g = 9.81 m/s^2, or 32 ft/s^2. THEREFORE, if you use meters for height, you should use the approximate value of g = 10 m/s^2. So, in this case a = = 5 (the numerical value). ALTERNATIVELY, if you use feet for height, you should use the approximate value of g = 32 ft/s^2. So, in this case a = = 16 (the numerical value). (d) To find the height at the time moment "t", simply substitute the value of "t" into the formula (1) and calculate. (e) To find the time "t" when the height has a given value h = , substitute h = into equation (1) and solve equation h(t) = -at^2 + bt + c = . (2) (f) To find the time when the height is maximal, use the formula = . (3) (g) To find the maximal height, substitute the time value t= of the formula (3) into the formula (1).

That's all you need to know.

        After my explanations, you can solve the problem on YOUR OWN now,
        but for it, you should have your governing equation written correctly.

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

To see numerous examples of solved problems, look into the lessons
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform
    - A flare is launched from a life raft vertically up
in this site.

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Question 1209340: Tony is three times as old as Gloria. Six years ago, Tony was five times as old as Gloria. Find the present ages of Tony and Gloria.

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
Tony is three times as old as Gloria. Six years ago, Tony was five times as old as Gloria.
Find the present ages of Tony and Gloria.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let Tony's age be x years; Then Gloria 's age is 3x years, according to the problem. Six years ago, Tony was (x-6) years old (1) Gloria was 3x-6 years ago. (2) We equate 5 times value of (1) and value of (2) 5(x-6) = 3x - 6. This is your setup equation. Simplify and find x 5x - 30 = 3x - 6 5x - 3x = 30 - 6 2x = 24 x = 24/2 = 12. ANSWER. Tony is 12 years old. Gloria is 3x = 3*12 = 36 years old. CHECK. 6 years ago their ages were 6 and 30 years, with the ratio 30/6 = 5. ! correct !

Solved.

Question 1209339:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

Empty post.

Question 1209254: Kylan is four times as old as Ella. Quentin is one year younger than Kylan and five years older than Ella.

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
Kylan is four times as old as Ella. Quentin is one year younger than Kylan and five years older than Ella.
~~~~~~~~~~~~~~~~~

Let x be the Ella's age, in years. Then Kylan age is 4x years. Quentin age is, from one side, 4x-1 years, and from the other side, x+5 years. It gives this equation 4x - 1 = x + 5. Solve it, step by step 4x - x = 5 + 1 3x = 6 x = 6/3 = 2. ANSWER. Ella is 2 years old; Kylan is 4*2 = 8 years old; Quentin is 8-1 = 7 years old.

Solved.

Question 1209191: Amy is 24 years younger than Vicky, and Vicky is 5 times as old as Amy this year

Found 4 solutions by ikleyn, josgarithmetic, timofer, math_tutor2020:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.
Amy is 24 years younger than Vicky, and Vicky is 5 times as old as Amy this year
~~~~~~~~~~~~~~~~~~~~~~~~~~~

The words "this year" are excessive in this post.

Excessive words in Math problems always smell bad.

Instead of including unnecessary excessive words, you would better
attach your question to the problem to make it meaningful.

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
A, Amy
V, Vicky

Substituting for A, into second equation

and you can use that to find Amy's age.

Answer by timofer(104)   (Show Source):
You can put this solution on YOUR website!
Both parts are for Now or This Year.

a for Amy and v for Vicky
and

Amy's age

Vicky

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

x = Amy's current age
x+24 = Vicky's current age

This year Vicky's age is 5 times that of Amy's age
Vicky = 5*Amy
x+24 = 5x
24 = 5x-x
24 = 4x
4x = 24
x = 24/4
x = 6
Amy is currently 6 years old.

x+24 = 6+24 = 30
Vicky is currently 30 years old.

Question 1209176: A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.
Found 3 solutions by josgarithmetic, greenestamps, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source):
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SPEED TIME DISTANCE A to B 4 d/4 d B to A 6 d/6 d TOTAL 0.75

Question asks for the TOTAL, or 2d.

Answer by greenestamps(13200)   (Show Source):
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The response from the other tutor shows a few methods for solving the problem which are all variations of the standard algebraic method.

Here is a non-standard and very different method which I personally prefer for solving this particular kind of problem.

The distances both directions are the same; the ratio of the speeds in the two directions is 4:6 = 2:3. That means that the ratio of times at the two speeds is 3:2.

The ratio of the time spent at 4 km/h to the time spent at 6 km/h is 3:2, and the total time is 45 minutes. Use mental arithmetic or any formal process you want to find that he spent 27 minutes at 4 km/h and 18 minutes at 6 km/h.

The number of kilometers traveled at 4 km/h for 27 minutes or 9/20 hours is 4*9/20 = 36/20 = 1.8.

So the distance traveled from A to B and back is 2*1.8 = 3.6 km.

ANSWER: 3.6 km (total distance traveled)

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For tutor @math_tutor2020....

Your calculations all show that 1.8km is the ONE WAY distance, not the total distance traveled....

Answer by math_tutor2020(3817)   (Show Source):
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Answer: 3.6 km

Work Shown

distance = rate*time
d = r*t

Going from A to B
d = r*t
d = 4*t
t = d/4

It takes d/4 hours to travel from A to B at a speed of 4 km/hr, where d is the distance from A to B.

Similar steps will show that it takes d/6 hours to travel from B to A at a speed of 6 km/hr.
This assumes the person took the same route to go back to A, or they took a route of equal length.

The two time values must add to 45 minutes = 45/60 = 3/4 of an hour.
Use the hour value because d/6 and d/4 are in hours.

(d/4) + (d/6) = 3/4
12*( (d/4) + (d/6) ) = 12*(3/4)
12*(d/4) + 12*(d/6) = 12*(3/4)
3d + 2d = 9
5d = 9
d = 9/5
d = 1.8 km exactly. This value hasn't been rounded.
This is the one-way distance.
The round trip distance is double that and it is 2*1.8 = 3.6 km

Another way to solve
(d/4) + (d/6) = 3/4
(3d/12) + (2d/12) = 3/4
(3d+2d)/12 = 3/4
5d/12 = 3/4
5d*4 = 12*3
20d = 36
d = 36/20
d = (9*4)/(5*4)
d = 9/5
d = 1.8 is the one-way distance; which doubles to a round trip distance of 3.6 km

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Another approach is to convert each km per hr speed value into km per min.
To do so, divide by 60.
4 km per hr = 4/60 = 1/15 of a km per min
6 km per hr = 6/60 = 1/10 of a km per min

Using d = r*t, we get this equation when going from A to B
d = (1/15)*t
which can be rearranged to
t = 15d
This is the time it takes, in minutes, to travel from A to B.

Similar steps will show it takes 10d minutes to travel from B to A.

Total travel time = 15d+10d = 25d = 45 min
25d = 45
d = 45/25
d = (9*5)/(5*5)
d = 9/5
d = 1.8 km is the one-way distance which doubles to 3.6 km and it's the final answer.

Edit: tutor greenestamps makes a great point. I had a brainfart for some reason. My error has been fixed (changed the answer from 1.8 km to 3.6 km)

Question 1208658: Question
Write in slope-intercept form an equation of the line that passes through the given points. (-9,5) (-3,3)
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source):
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basic slope-intercept form

Choose one of the points, maybe, (-3,3).

and using the chosen point,

The equation wanted is

Answer by math_tutor2020(3817)   (Show Source):
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Let's find the slope.

The slope is -1/3 which means go down 1 and then right 3.

Next apply the point-slope template.

Plug in the slope.

Plug in one of the point's coordinates.

is the final answer

Question 1207798: Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twices maris's age
Found 6 solutions by mccravyedwin, MathTherapy, greenestamps, ikleyn, josgarithmetic, MathLover1:
Answer by mccravyedwin(407)   (Show Source):
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I suspect that a lot of grammatical and spelling errors we find in these problems posted on here are not due to students' carelessness. I think it may be because these students live in a country where English is not the main language, and they are translating their problems from their language into English as best they can. Edwin

Answer by MathTherapy(10552)   (Show Source):
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Rico's and Maris's age gap is 25 years. 4 years from now, Rico's age will be 5 years less than twices maris's age The CORRECT answer, whatever that may be, DEPENDS on whether "4 years from now, Rico's age will be 5 years less than twices maris's age," should acually be: 4 years from now, Rico's age will be 5 years less than ~~twices maris's~~ twice Maris' age, THEN OR 4 years from now, Rico's age will be 5 years less than ~~twices maris's~~ twice Maris' CURRENT age If the former, current ages are 26 and 51 If the latter, current ages are 34 and 59, with Rico OBVIOUSLY being older (2^nd sentence confirms this).

Answer by greenestamps(13200)   (Show Source):
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The age gap will always be 25 years....

From the given information....
Let x = Maris's age 4 years from now
Then 2x-5 = Rico's age 4 years from now

The difference in ages 4 years from now (and always) is 25 years:

(2x-5)-x=25
2x-5-x=25
x=30

Maris's age 4 years from now: x = 30
Rico's age 4 years from now: 2x-5 = 55 (or x+25 = 55)

We don't know what the answers are, because you didn't ask a question....

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Added later, after seeing other responses....

In the editorial comment at the end of her response, tutor @ikleyn implies that you have failed to solve the problem correctly if you didn't use an absolute value equation to represent the given information that the "age gap is 25 years".

That is not true, because the information in the second sentence tells you that Rico is older. So, assuming you read the whole question before starting the work of solving the problem, an absolute value equation is not needed.

Answer by ikleyn(52787)   (Show Source):
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.
Rico's and Maris's age gap is 25 years.
4 years from now, Rico's age will be 5 years less than twice maris's age.
~~~~~~~~~~~~~~~~~~~~~~~~

        The question absents, which is   .

        In the post by @MathLover1, the solution is not complete.
        I came to bring a complete analysis.

As you read the problem, it produces two equations. |R-M| = 25 (1) ("the gap is 25 years") R+4 = 2(M+4)-5 (2) ("4 years from now") Notice that equation (1) is an absolute value equation. So, equation (1) is equivalent to system of two equations R - M = 25 (1a) or R - M = -25 (1b) It means that we should consider two cases and solve two associated systems. One system is R - M = 25, (1a) R + 4 = 2(M+4)-5. (2) Another system is R - M = -25, (1b) R + 4 = 2(M+4)-5. (2) Let start solving first system. From equation (2), R = 2M - 1. (3) Substitute it into equation (1a) (2M-1) - M = 25. It implies 2M - M = 25 + 1 M = 26. Substitute it into equation (3) R = 2M - 1 = 2*26 - 1 = 51. So, Maris is 26 years old; Rico is 51 years old. At this point, we complete working with the first system and start working with the second system. We again substitute (3) into equation (1b) (2M-1) - M = -25 M = -25 + 1 = -24. The age is always positive, it can not be negative, so we deny this possibility, at all. ANSWER. The problem has a unique solution: Maris is 26 years old; Rico is 51 years old.

Solved in full and completely.

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

The lesson to learn.

        The term " gap between two values " means the absolute value of the difference.

        So, the system of equations should include an absolute value equation.

        In some sense, this problem is a TRAP, and if you did not recognize this trap
        with the absolute value equation, then you failed.

/////////////////////

Added later, after seeing comment by @greenestamps to my solution.

The problem says

Rico's and Maris' age gap is 25 years. 4 years from now, Rico's age will be 5 years less than twice maris' age.

In his comment, @greenestamps writes " the information in the second sentence tells you that Rico is older".

But the problem does not say it explicitly. It says something different.

It becomes clear not from this sentence, but from analysis of the full system of equations.

So, the meaning of this @greenestamps' comment is dark to me.
I do not agree with it, and I do not think that it is correct.

\\\\\\\\\\\\\\\\\\\

To post by Edwin.

        Edwin, can you explain, please, how your post helps us to treat this problem ?

Edwin, offhand I requested Google for these keywords

        "Rico's and Maris's age gap is 25 years.
        4 years from now, Rico's age will be 5 years less than twices maris's age".

I got several references/links

https://math.he.net/question/1d4c2a3ddd3855cf85182d952bc3247db2813e73

https://www.facebook.com/photo.php?fbid=997207245743634&id=100063631043464&set=a.518642723600091

https://www.gauthmath.com/solution/1805163005838341/Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-the-break

https://www.gauthmath.com/solution/1805071070479366/PROBLEM-Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-t

So, I am very far from assuming that poor unfortunate foreign visitors send
this problem everywhere in the Internet out of curiosity and desire for knowledge.

My hypothesis is that they either participate in training AI or
fill some other web-sites this way by collecting solutions from everywhere.

All what they really do, is copying, pasting and submitting, without reading;
therefore, they even do not notice when they miss the question.
They simply do not read what they post.

Because making sense is not a goal of their job, at all.

Their job is copy/paste/submit and do it fast - nothing more.

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
Rico and Maria, age difference 25 years

Literal of description:

simple steps, transform to

Assuming Rico is older than Maria,

substitute:

Meaning .

Answer by MathLover1(20850)   (Show Source):
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.

let Rico's age be and Maris's age
if Rico's and Maris's age gap is years, we have
.......eq.1
if years from now, Rico's age will be years less than twices maris's age, we have

.........eq.2
go to
.......eq.1, substitute

go to
.........eq.2, substitute

answer:
Rico is and Maris is

Question 1207790: Jon is 4 years older than twice the age of his youngar sister, Alice. The sum of the spas in 25 years. How old are John and Auce?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617)   (Show Source):
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Jon,
Alice,

AGE SUM, ---------------, Alice

, Jon

Answer by MathLover1(20850)   (Show Source):
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let Jon's age be and Alice’s age be
if Jon is years older than twice the age of Alice, we have

........eq.1

if the sum of the spas in years, we have
...eq.2

substitute from eq.1 in eq.2

...eq.2, solve for

go to eq.1, substitute

........eq.1

so, Jon is years old and Alice is years old

Question 1207400: Kenneth's father is 36 years older than he is. In 7 years' time, his father will be double Kenneth's age. How old is Kenneth's father now?
Answer by greenestamps(13200)   (Show Source):
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A formal algebraic solution....

Let x be the age of Kenneth's father
Then x-36 is Kenneth's age

x+7 = father's age in 7 years
(x-36)+7 = x-29 = Kenneth's age in 7 years

In 7 years, the father's age will be twice Kenneth's age:

x+7=2(x-29)
x+7=2x-58
65=x

ANSWER: 65

CHECK: x+7=65+7=72; x-29=65-29=36; 72=2*36

Informally (using logical reasoning and simple mental arithmetic, which is good exercise)....

The difference in their ages is 36; when the father is twice as old, their ages will be 72 and 36. That will be 7 years from now, so the father's age now is 72-7 = 65

Question 1207340: Angelica has 84 bills consisting of ₱10 and ₱50. If the total amount of her money is ₱3250, how many pieces of each kind of bill does she have?

Answer by ikleyn(52787)   (Show Source):
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.
Angelica has 84 bills consisting of ₱10 and ₱50. If the total amount of her money is ₱3250,
how many pieces of each kind of bill does she have?
~~~~~~~~~~~~~~~~~~~~~~~~~

        The problem is posed INCORRECTLY
        and has no solutions in integer positive number of bills.

Indeed, it is clear that the total of 84 bills of P10 and P50 should be multiple of P20;
but 3250 is not a multiple of 20.

So, the situation described in this post, may NEVER happen in real life.