Questions on Word Problems: Age answered by real tutors!

You can put this solution on YOUR website!
Let
Present age of Shelly = x
Present age of Michele = x-3

Given
======
Four years ago
Shelly was = x-4
Michele was = (x-3)-4 = x-3-4 = x-7
Then
the sum of their ages was 71.
(x-4)+(x-7)=71
x-4+x-7=71
2x-11=71
2x=71+11
2x=82
2x/2=82/2
x=41

Present age of Shelly = x = 41 years old
Present age of Michele = x-3 = 41-3 = 38 years old



(Example 3. Use the information in the table below showing algebraic expressions in terms of x.)

No table given

You can put this solution on YOUR website!
within eleven years, the age of peter will be half the square of the age he was 13 years ago. calculate the current age of peter...
---------------
p-11 = (1/2)(p-13)^2
2p-22 = p^2-26p+169
------
p^2-28p+191 = 0
----
Usable solution to avoid negative age:
p = 16.2361
===============
Cheers,
Stan H.

You can put this solution on YOUR website!
why use guess n check? that will take longer
John(j) and Bill(b)


.





.




.
check



correct
check



correct

You can put this solution on YOUR website!
The ratio of their ages should decrease with time, but you could not calculate the answer ratio without more information.
Depending on what class you are in, you would justify that the ratio decreases in a different way, but for a multiple choice problem, you would not need to prove it.
The ratios shown, calculated by dividing (rounding if needed) are:
=1.25
=1.375
=1.286 (rounded)
=1.154 (rounded)
=1.267 (rounded)
The only answer choice that is less than is 15:13
If you are curious (and want to know if it makes sense), making the current age of the wife , the current age of the husband would be , so after 20 year the ratio would be
--> --> --> -->
That would make the wife 32 years old and the husband at the time. It is likely that they would both be alive 20 years later and would be 52 and 60, and the ratio of their ages then would be

You can put this solution on YOUR website!
let
Present age of Suzan = s
Present age of Ray = r

Suzan is 7years older than her brother Ray
s=r+7............(1)
Sum of their ages is 41
s+r=41.........(2)

Put the value of s from (1) to (2)

r+7+r=41
2r=41-7
2r=34
2r/2=34/2
r=17

Put the value of r in (1)
s=r+7
s=17+7
s=24

Present age of Suzan = s = 24 years old
Present age of Ray = r = 17 years old

You can put this solution on YOUR website!
Let the time to drain the pool for 2nd pump =
The 1st pump's rate of draining is
which means ( 1 pool ) / ( 9 min )
The 2nd pump's rate of draining is
which means ( 1 pool ) / ( t minutes )
Together, their rate of draining is
------------------------------
To find the rate when both are used, add their
individual rates

Multiply both sides by




The 2nd pump can drain the pool in 11 min and 15 sec
operating alone

You can put this solution on YOUR website!
Their were 3 brothers. The product of their ages is 36. the sum of their ages is equal to the age of the only sister.
the 3 brothers never admit their ages but the sister always admits her own
even so you need to know that the oldest brother usually wears his baseball cap backwards.
How old is each brother? explain
:
That last sentence makes me think that perhaps the two youngest are twins, the same age.
Call the oldest brother age = a, the twin brothers age, b
:
"The product of their ages is 36."
a * b * b = 36
ab^2 = 36
b^2 =
b =
:
There are two integer solutions to this equation where a is older than b
a=9, b=2; but a two year old probably would not worry about admitting their age
and
a=4, b=3; reasonable solutions,
The oldest is 4, the twin brothers are 3,
:
"the sum of their ages is equal to the age of the only sister."
s = a + 2b
the sister would be 10

You can put this solution on YOUR website!
"The sum of the present ages of Eric and his father is 65 years" ___ E + f = 65 ___ f = 65 - E

"In 8 years, his father will be twice as old as Eric will be at that time" ___ f + 8 = 2(E + 8)

substituting ___ (65 - E) + 8 = 2E + 16 ___ 57 = 3E

solve for E, then substitute back to find f

You can put this solution on YOUR website!
Ten years from now, A will be twice as old as B. Five years ago, A was three times as old as B. What are the present ages of A and B?
----
Equations:
(A+10) = 2(B+10)
(A-5) = 3(B-5)
------
Rearrange:
A - 2B = 10
A - 3B = -10
----
Subtract and solve for "B":
B = 20
----
Solve for "A":
A = 2B+10
A = 2*20+10
A = 50
==================
cheers,
Stan H.

You can put this solution on YOUR website!
A man is 42 years old and his daughter is 8. In how many years will the father be twice as old?
--------
The age difference is 34 (42 - 8)
When she's 34, he'll be 68

You can put this solution on YOUR website!
Let = Aaron's age now
Let = Baron's age now
= Aaron's age in 5 yrs
= Baron's age in 5 yrs
---------------
given:
(1)
(2)
-------------------------
(2)
(2)
(2)
and
(1)
(1)
Subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
(1)
(1)
Aaron is 14 and Baron is 11
check:
(2)
(2)
(2)
(2)
(2)
OK

You can put this solution on YOUR website!
martha is 24 years old. susan is at least 4 years younger than martha. if susan is k years old write an inequality showing susans age.
-----------------
m = 24
s <= m-4
---
k <= m-4
===============
Cheers,
Stan H.

You can put this solution on YOUR website!
m=my age d=daughter age

im going to explain the above equation as its second nature for me but for some this may be hard to get this equation from words:
1) the is same as "5 years ago the sum of my age and my daughters age" and are the present ages so subtracting 5 years from each of them makes it 5 years ago
2) is same as "the average of the present ages of my daughter and my self" average is adding both ages and dividing them by the number of ages added
3) is same as "five times the average of the present ages of my daughter and my self" multiplying by 5
4) is same as "a third of five times the average of the present ages of my daughter and my self" multiplying by a third

.
.
"my daughter will be 15 years old in 5years" so
who is tim?
dumb question we dont know who tim is and what tim's age is so its an incomplete question but if you wanted to find your age it is as follows.
substitute for
solve for
add like terms and distribute the and
multiply by and subtract from each side

.
check




correct

You can put this solution on YOUR website!
Dan's brother is 1/2 his father's age. His brother is 22 years old. How old is his father?
----
b = (1/2)f
b = 22
---
Equation:
22 = (1/2)f
father = 2*22 = 44 yrs old
==============================
Cheers,
Stan H.

You can put this solution on YOUR website!
Let
Present age of Anna = a
Present age of Brandi = b


Given
=====
Anna is seven years younger than Brandi
a=b-7............(1)
Three years from now
Anna will be = a+3
Nine year ago
Brandi was = b-9

Then

Anna will be twice as old as brandi was nine years ago
a+3=2(b-9)
a+3=2b-18
a=2b-18-3
a=2b-21................(2)
Put the value of a from (1) to (2)
b-7=2b-21
b-2b=-21+7
-b=-14
Multiply by -1 both sides of above equation
(-1)(-b)=(-1)(-14)
b=14
Put the value of b in (1)
a=b-7
a=14-7
a=7
Present age of Anna = a = 7 years old
Present age of Brandi = b = 14 years old
Six years from now Brandi will be = 14+6 = 20

You can put this solution on YOUR website!
Since 7 years ago he was half the age of 12 that means that he was 6. But he was 6 seven years ago. So to figure out how old he is now you have to add 7 to 6 and you get 13. The answer is 13 years old

This is how old he was seven years ago. 12/2=6 This is how old he is now. 6+7=13

You can put this solution on YOUR website!
Let's first pick a person to be our variable; how about Ryan. Ryan will be "x".
Now, they're asking you to turn this sentence into an equation. Start by looking at the solid number that you already know: Ryan's sister is 14. So that will be the lonely number on one side of the equal sign. Now look at the first part of the sentence: Ryan's sister is 2 years less than twice his age. This means that twice Ryan's age(2x) minus two(2x-2) will be equal to Ryan's sister's age.
2x-2=14
Add 2 to both sides.
2x=16
Divide both sides by 2 to get the variable(letter) alone.
x=8
Ryan is 8 years old.
You don't even need to solve it, just have the equation, if you're "translating" it.
Another way to think about this is by breaking apart the sentence(if you put it into words, it would look something like "Ryan's sister=2(ryan)-2".
Hope this helps :)

You can put this solution on YOUR website!
Let Mary's age be .
She cuts flowers the first day, flowers the second day, the third day, the fourth day and the fifth day.
The numbers of flowers cut each day form a geometric sequence (or geometric progression), but we do not care about that until Algebra 2 (in the USA).
What's important is that on the fifth day she cut flowers and that number is the same as her grandmother's age plus Mary's age: . So
--> --> --> -->

You can put this solution on YOUR website!
5b = 7a

3(b + 4) = 4(a + 4) ___ 3b + 12 = 4a + 16 ___ 21b + 84 = 28a + 112

subtracting 4 times first eqn ___ 21b + 84 - 20b = 28a + 112 - 28a ___ b = 28

You can put this solution on YOUR website!
f = 41

s = 9

f + x = 3(s + x) ___ 41 + x = 3(9 + x) ___ 41 + x = 27 + 3x ___ 14 = 2x

You can put this solution on YOUR website!
A 24 year old woman is now six times as old as her son; someday she will be only three times as old as he is. What will be her age when this occurs?
=========================
At present, the mother is 24 which is 6 times older than her son. Therefore, her son is now 4.
x years in the future, the mother will be 3 times older:
24 + x = 3(4 + x)
24 + x = 12 + 3x
2x = 12
x = 6
Therefore, the mother will be 24+6 = 30 yrs old when this occurs (the son will be 10)

You can put this solution on YOUR website!
If you jump from 10 to 100, then you're adding 90 years. So the answer is 5+90 = 95

You can put this solution on YOUR website!
Mary is five less than three times as old as sue. If the sum of their ages is 23, how old is mary?
------
Equations:
m + s = 24
m = 3s-5
---
Substitute for "m" and solvd for "s":
3s-5 + s = 24
4s = 29
Sue = (29/4) yrs
---------------------
Solve for "m":
m + (29/4) = 24
----
4m + 29 = 96
4m = 67
Mary = (67/4) years
====================
Cheers,
Stan H.
============

You can put this solution on YOUR website!
I am 10years old and you are half
my age(5) when I'm 100 years old how old will u
be?????
----
You are 5 years younger than me.
You will be 95 when I am 100.
Cheers,
Stan H.

You can put this solution on YOUR website!
Let
Present age of Skyler = s
Present age of Jason = j
Given
Skyler is 20 years older than Jason
s=j+20.................(1)
In 8 years
Skyler will be = s+8
Jason will be = j+8
Then
Skyler will be twice as old as Jason
s+8=2(j+8)
s+8=2j+16
s=2j+16-8
s=2j+8..............(2)
Put the value of s from (1) to (2)
j+20=2j+8
j-2j=8-20
-j=-12
Multiply by -1 both sides
(-1)(-j)=(-1)(-12)
j=12
Put the value of j in (1)
s=j+20
s=12+20
s=32

Present age of Skyler = s = 32 years old
Present age of Jason = j = 12 years old

You can put this solution on YOUR website!
Both digits are the same. It is less than 50. The sum of its digits is 6
------------
6/2 = 3
-----------
"Both digits are the same." Can one digit be the same?

You can put this solution on YOUR website!
Let u = the units digit of the original number
Let t = the tens digit
The number can be written as 10t + u
Given: Sum of the digits is 10. When the digits are reversed, the number is increased by 72.
t + u = 10 -> u = 10 - t
10u + t = 10t + u + 72
9u - 9t = 72
9(10-t) - 9t = 72
Solve for t:
90 - 18t = 72
18t = 18
t = 1
Therefore, u = 9
So the number is 19
Check:
91 = 19 + 72

You can put this solution on YOUR website!
let x equal the aunt's age.
let y equal the niece's age.
the niece is currently 1/3 the age of the aunt.
the equation for that is:
y = x/3
if we solve this equation for x, we get:
x = 3y
6 years ago the aunt's age was 5 times the niece's age.
the equation for that is:
x - 6 = 5 * (y - 6)
since we have y = x/3 and we have the equivalent equation of x = 3y, we can substitute either in the equation of x - 6 = 5 * (y - 6) to eliminate one of the unknowns in that equation.
we'll use x = 3y because it seems to make the calculations easier.
the equation of:
x - 6 = 5 * (y - 6) becomes:
3y - 6 = 5 * (y - 6)
simplify this to get:
3y - 6 = 5y - 30
subtract 3y from both sides of this equation and add 30 to both sides of this equation to get:
24 = 2y
divide both sides of this equation by 2 to get:
12 = y which is the same as:
y = 12
since x = 3y, this makes x = 36
x is the aunt's age.
y is the niece's age.
the aunt is 36 years old today.
the niece is 12 years old today.
6 years ago the aunt was 30.
6 years ago the niece was 6.
6 years ago the aunt was 5 times as old as the niece.
today the niece is 1/3 as old as the aunt.
it all checks out, so the answer is:
josie is 36 years old.
dianne is 12 years old.
josie is the aunt.
dianne is the niece.

You can put this solution on YOUR website!
a father is twice older than his son and the sum of their ages is 48.How old is each?
-----------
Twice = 2 times
2 times older = 3 times as old
--> 12 & 36

You can put this solution on YOUR website!
let mary's age be x years
On 5 days she cuts x flowers and makes a bouquet
she cut 5x flowers
5x = 60
/5
x= 12
Here age is 12 years

You can put this solution on YOUR website!
2 years gao Nathalie ---x years
Anton 3x
After 4 years
Nathalie will be x+6
Anton 3x+6
3x+6 =2(x+6)
3x+6 =2x+12
3x-2x=12-6
x=6
2 years ago Nathalie was 6 years
now she is 8 years
Anton was 3x years = 3*6 = 18.
so he wil be 20 years now

You can put this solution on YOUR website!
Let
Present age of Marilyn = m
Present age of Rosie = r


Marilyn is three years younger than her friend Rosie
m=r-3..............(1)
Five years ago
Age of Marilyn was = m-5
Age of Rosie was = r-5
In seven years
Age of Marilyn will be = m+7
Age of Rosie will be = r+7
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
(m+7)(r+7)=6[(m-5)(r-5)]-2
mr+7m+7r+49=6(mr-5m-5r+25)-2
mr+7m+7r+49=6mr-30m-30r+150-2
mr-6mr+7m+30m+30r+7r=150-2-49
-5mr+37m+37r=150-51
-5mr+37m+37r=99..................(2)
Put the value of m from (1) to (2)
-5(r-3)r+37(r-3)+37r=99
-5r^2+15r+37r-111+37r=99
-5r^2+89r-99-111=0
-5r^2+89r-200=0
Now solve for r

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=3721 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.8, 15. Here's your graph:

r=15 or r = 2.8 (reject)
Put r=15 in (1)
m=r-3
m=15-3
m=12

Present age of Marilyn = m = 12 years old
Present age of Rosie = r = 15 years old


Check
======
Five years ago
Age of Marilyn was = 7
Age of Rosie was = 10
In seven years
Age of Marilyn will be = 19
Age of Rosie will be = 22
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
19*22=6(7*10)-2
418=6(70)-2
418=420-2
418=418

You can put this solution on YOUR website!
let the tens digit =
Let the units digit =
The actual number is
The number with the digits reversed is
given:
(1)
(2)
------------
Multiply both sides of (2) by
(2)
(2)
(2)
(2)
(2)
(2)
Substitute (2) into (1)
(1)
(1)
(1)
(1)
and, since
(1)
(1)
(1)
The original number is 72
check answer:
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
OK
Note that the answer is impossible,
since the digits have to add up to

You can put this solution on YOUR website!
Rose is 29 Years old. Her mother is 50.
How many years ago was the mother twice as old as Rose?
:
Let y = no. of years for this to be true
:
50-y = 2(29-y)
50 - y = 58 - 2y
- y + 2y = 58 - 50
y = 8 yrs ago
;
:
See if that is true, 8 yrs ago:
Mom will be 42
Rose will be 21

You can put this solution on YOUR website!
In a three-digit number, the digit at the hundreds place is three times the digit at the ones place and the sum of the digits is 15. If the digits are reversed, the number is reduced by 396. Find the number (Ans. 672)
**
let u=units digit
let t=tens digit
let h=hundreds digit
..
h=3u
u+t+h=15
original number: 100h+10t+u
reversed number:100u+10t+h
original number-reversed number=396
(100h+10t+u)-(100u+10t+h)=396
100h+10t+u-100u-10t-h=396
99h-99u=396
99(3u)-99u=396
2u*99=396
u=396/2*99=2
h=3u=6
t=15-t+h=15-8=7
ans:
number: 672

You can put this solution on YOUR website!
The ratio of a two-digit number and the number and the number obtained by interchanging the digits is 4:7. If the difference of the digits is 3. Find the number. (Ans. 36)
**
let u=units digit
let t=ten's digit
original number=10t+u
interchanged number=10u+t
u-t=3
u=3+t
..
(10t+u)/(10u+t)=4/7
70t+7u=40u+4t
66t=33u=33(3+t)=99+33t
33t=99
t=3
u=3+t=6
ans:
number=tu=36

You can put this solution on YOUR website!
Boat speed =x km/h
current speed =y km/h
against current x-y 3.00 hours
with current x+y 2.00 hours

Distance = same= 50 km
t=d/r
50/(x-y )=3.00
3(x-y)= 50.00
3x-3y= 50 ....................1
50/(x+y )=2.00
2.00(x+y)=50
2.00x+2.00y=50 ...............2
Multiply (1) by 2.00
Multiply (2) by 3.00
we get
6x-6y = 100
6x+6y = 150
12x=250
/12
x = 125/6 km/h

plug value of x in (1)
3 x -3 y = 50
125/2 -3 y = 50
-3 y = 50 -125/2
-3 y = -25/2
y = 25/6 km/h
The speed of Boat = 125/6 km/h
The speed of current = 25/6 km/h
m.ananth@hotmail.ca

You can put this solution on YOUR website!
Kim is 3 times as old as she was 2 years ago.
How old is she now?
:
Let a = Kim's present age
;
a = 3(a-2)
a = 3a - 6
6 = 3a - a
6 = 2a
a = 3 yrs old now

You can put this solution on YOUR website!
Let = Jon's age now
= Jon's age 7 yrs from now
= Jon's age 11 yrs from now
= Jon's age 5 yrs from now
given:






In 5 yrs I will be 90
check:





OK

You can put this solution on YOUR website!
x+y = 66
y = x+6


x+y = 66

x+x+6 = 66

2x+6 = 66

2x = 66-6

2x = 60

x = 60/2

x = 30

y = x+6

y = 30+6

y = 36


So the two ages are 30 and 36


-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

You can put this solution on YOUR website!


Impossible. As two people age, the fractional relationship between their ages increases, but in this problem 1/6 is smaller than 1/4.

John

My calculator said it, I believe it, that settles it

You can put this solution on YOUR website!
Benilda is one year older than twice her sister's age
Benilda's age will be b and her sister's age will be s.
When we see the word "is", we know to put an equal sign
b=2s+1
The difference of their ages is 18.
b-s=18
We are going to use subsitution because the first equation is already solved for b.
(2s+1)-s=18
combined like terms
s+1=18
subtracted 1 from both sides
s=17
and then we can plug in 17 in for s
b=2*17+1
b=35

You can put this solution on YOUR website!
Let = Alfred's age now
= Alfred's age 6 yrs ago
Let = his brother's age now
= brother's age 6 yrs ago
--------------------------------------
given:
(1)
(2)
--------------------------------------
(2)
Subtract from both sides
(2)
(2)
and
(1)
(1)
Alfred is 36 now, and
his brother is 12 now