Question

The ages of A and B are in the ratio 5:3. After 6 years, their ages will be in the ratio 7:5.
The present age of A is
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Answer 1

A:B = 5:3

This can also be expressed as a fraction, when the given values are reduced (for example, 21/15):

A/B = 5/3

You can solve for either A or B here, but let’s solve for A

First, multiply both sides by B:

A = (5b)/3

In the second equation, A and B both increase by 6:

(A+6)/(B+6) = 7:5

recall that A = 5b/3

So substitute for A in the first equation:

((5b/3)+6)/(B+6) = 7:5

Multiply both sides by (b+6) to get rid of the denominator

((5b/3)+6) = (7(B+6)/5

Now, expand the parentheses on the right side:

((5b/3)+6)=(7b+42)/5

Drop the parentheses on the left side

(5b/3)+6 = (7b+42)/5

Multiply both sides by 15 to get rid of both denominators

15(5b/3)+15*6 = 15(7b+42)/5

(75b/3)+15*6 = 3(7b+42)

Use FOIL on the right side:

(75b/3)+15*6 = 21b+126

25b + 90 = 21b + 126

Subtract 21b from both sides, then subtract 90 from both sides:

4b = 36

Divide by 4:

b = 9

Now go back to the very first equation and pop in 9 for b:

A:B = 5:3

b = 9

A/9 = 5/3

Multiply both sides by 9:

A = 45/3

A = 15

Now go back to the second equation from the question and substitute and see if it fits:

(A+6)/(B+6) = 7/5

(15+6)/(9+6)=7/5

21/15 = 7/5

7/5 = 7/5

So the ages are 15 and 9.

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