SOLUTION: Tom is 15 years younger than alice. Ten years ago, Alice was 4 times as old as Tom was then. How old is each now?

Question 410551: Tom is 15 years younger than alice. Ten years ago, Alice was 4 times as old as Tom was then. How old is each now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = tom's age today
x + 15 = alice's age today.

ten years ago, alice was 4 times as old as tom was then.

ten yeara ago, tom was x-10 years old.
ten years ago, alice was (x+15) - 10 = x+5 years old.

ten years ago, alice was 4 times as old as tom was then.

x+5 = 4*(x-10)

simplify to get:

x+5 = 4x - 40

subtract x from both sides of the equation to get:

5 = 3x - 40

add 40 to both sides of the equation to get:

45 = 3x

divide both sides of the equation by 3 to get:

x = 15

that's how old tom is today.

alice is 15 years older than that which makes alice 30 years old today.

ten years ago, tom was 5.
ten years ago, alice was 20.

20 is 4 * 5 which confirms the value of x is good.

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