SOLUTION: the sum of the ages of peter and paul is 24. five years ago their respective ages were in the ratio 3:4. how old will they be in 3 years' time?

Question 1171264: the sum of the ages of peter and paul is 24. five years ago their respective ages were in the ratio 3:4. how old will they be in 3 years' time?
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
x = Peter's present age
y = Paul's
Write an equation for each statement
:
the sum of the ages of peter and paul is 24.
x + y = 24
five years ago their respective ages were in the ratio 3:4.
=
cross multiply
4(x-5) = 3(y-5)
4x - 20 = 3y - 15
4x = 3y - 15 + 20
4x = 3y + 5
4x - 3y = 5
:
Use elimination with 1st equation, multiply it by 3
3x + 3y = 72
4x - 3y = 5
----------------addition eliminates y find x
7x = 77
x = 77/7
x = 11 years is Peter's age
and
11 + y = 24
y = 24- 11
y = 13 is Paul's age
:
how old will they be in 3 years' time?
Obviously, Peter will 14 and Paul will 16
:
:
Check their ages 5 yrs ago: =
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Given that their ages 5 years ago were in the ratio 3:4, start on the problem with this:

let 3x = Peter's age 5 years ago
let 4x = Paul's age 5 years ago

The sum of their ages now is 24.

3x+5 = Peter's age now; 4x+5 = Paul's age now.

Peter's age is 3x+5=11
Paul's age is 4x+5=13

ANSWERS:
Peter's age 3 years from now will be 11+3=14
Paul's age 3 years from now will be 13+3=16

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