SOLUTION: Could you please explain how to tackle this problem? The ratio of Jonathan’s age to David’s age is 6:5. In seven years it will be 7:6. What are their ages now. Thanks in adva

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Question 1085934: Could you please explain how to tackle this problem?
The ratio of Jonathan’s age to David’s age is 6:5. In seven years it will be 7:6. What are their ages now.
Thanks in advance.

Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of Jonathan’s age to David’s age is 6:5. In seven years it will be 7:6. What are their ages now.
================
J/D = 6/5 --> 5J = 6D
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(J+7)/(D+7) = 7/6 --> 6(J+7) = 7(D+7)
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5J = 6D
6(J+7) = 7(D+7)
---
Can you do the rest?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of Jonathan’s age to David’s age is 6%3A5.
let Jonathan’s age be x and David’s age y, then we have
x%3Ay=6%3A5
5x=6y
x=6y%2F5....eq.1

In seven years it will be 7%3A6:
%28x%2B7%29%3A%28y%2B7%29=7%3A6
6%28x%2B7%29=7%28y%2B7%29
6x%2B42=7y%2B49
6x=7y%2B49-42
6x=7y%2B7
x=7y%2F6%2B7%2F6.......eq2
from eq1 and eq2 we have
6y%2F5=7y%2F6%2B7%2F6......solve for y
5%286y%2F5%29=5%287y%2F6%29%2B5%287%2F6%29
6y=35y%2F6%2B35%2F6...both sides multiply by 6
36y=35y%2B35
36y-35y=35
highlight%28y=35%29
now find x
x=6y%2F5....eq.1
x=%286%2A35%29%2F5....simplify
x=%286%2Across%2835%297%29%2Fcross%285%291
x=6%2A7
highlight%28x=42%29
so,Jonathan’s age is highlight%2842%29 and David’s age is highlight%2835%29
check the ratios:
x%3Ay=6%3A5
42%3A35=6%3A5
1.2=1.2
in seven years Jonathan’s age will be 42%2B7=49, and David’s age will be 35%2B7=42
49%3A42=7%3A6
1.166666666666667=1.166666666666667

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Could you please explain how to tackle this problem?
The ratio of Jonathan’s age to David’s age is 6:5. In seven years it will be 7:6. What are their ages now.
Thanks in advance.
Let MULTIPLICATIVE factor of each person’s age be x

Then Jonathan’s age is: 6x and David’s is: 5x

We then get: %286x+%2B+7%29%2F%285x+%2B+7%29+=+7%2F6

6(6x + 7) = 7(5x + 7) ---------- Cross-multiplying 

36x + 42 = 35x + 49

36x – 35x = 49 – 42

x, or MULTIPLICATIVE factor of each person’s age is 7



It is that simple!!