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
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?
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