SOLUTION: The ratio of the ages of two sisters is 4 :3.The elder sister is 3 years older than the younger one. Find their ages.

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Question 1141879: The ratio of the ages of two sisters is 4 :3.The elder sister is 3 years older than the younger one. Find their ages.
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source):
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let a represent the age of the older sister.
let b represent the age of the younger sister.

the ratio of the older sister to the younger sister is 4:3.

you get a/b = 4/3

the older sister is 3 years older than the younger sister.

you get a = b + 3

in the equation of a/b = 4/3, replace a with b + 3 to get:

(b + 3) / b = 4 / 3

multiply both sides of this equation by b to get b + 3 = 4 * b / 3

multiply both sides of this equation by 3 to get 3 * b + 9 = 4 * b

subtract 3 * b from both sides of this equation to get 9 = 4 * b - 3 * b

combine like terms to get 9 = b.

that's the age of the younger sister.

the older sister is 3 years older, so the age of the older sister is 12.

you have a = 12 and b = 9, with a representing the age of the older sister and b representing the age of the younger sister.

the ratio of the age of the older sister to the age of the younger sister is equal to a / b which is equal to 12 / 9.

this can be simplified to 4 / 3, confirming the solution is good.

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Since the ratio of the two ages is 4:3, let the two ages be 4x and 3x.

In virtually all problems where a ratio is given, that is a good way to start on the problem.

The problem tells us that the difference in their ages is 3 years. But the difference in their ages is 4x-3x = x; so x=3.

And that makes the ages of the two sisters 4x=12 and 3x=9.