SOLUTION: The sum of the ages for Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old will they be in three years time?

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Question 1170973: The sum of the ages for Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old will they be in three years time?
Found 3 solutions by math_tutor2020, MathTherapy, josgarithmetic:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

E = peter's age right now
A = paul's age right now
Ages are in years.
I went with the second letter of their names since both started with P. Feel free to label your variables however you want.

"The sum of their ages is 24" means E+A = 24. We can solve for E to get E = 24-A.

Five years ago, their ages were E-5 and A-5
The ratio of these past ages was 3:4, which means we can say,
(peter's age 5 years ago)/(paul's age 5 years ago) = 3/4
(E-5)/(A-5) = 3/4
4(E-5) = 3(A-5) .... cross multiply
4E-20 = 3A-15
4(24-A)-20 = 3A-15 ... plug in E = 24-A
96-4A-20 = 3A-15
76-4A = 3A-15
76+15 = 3A+4A
91 = 7A
7A = 91
A = 91/7
A = 13

Paul is currently 13 years old. In three years time, he will be 13+3 = 16 years old.

E = 24-A
E = 24-13
E = 11

Peter is currently 11 years old. In three years time, he will be 11+3 = 14 years old.


Answers:
Peter will be 14 years of age
Paul will be 16 years of age
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

The sum of the ages for Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old will they be in three years time?
Let Peter's age be P

Then Paul's is: 24 - P

We then get: 

4(P - 5) = 3(19 - P) ------ Cross-multiplying 

4P - 20 = 57 - 3P

4P + 3P = 57 + 20

7P = 77

Peter or 

Paul's age: 

Can you now find their ages, 3 years from now? 

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
 r, peteR

L, pauL







-





-











-



-

-

In three more years:

 

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