SOLUTION: The ratio of Tom’s age to Mike’s age is 8:5. 30 years later, this ratio will be 6:5. How much older is Tom than Mike?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of Tom’s age to Mike’s age is 8:5. 30 years later, this ratio will be 6:5. How much older is Tom than Mike?      Log On


   

Question 1191182: The ratio of Tom’s age to Mike’s age is 8:5. 30 years later, this ratio will be 6:5. How much older is Tom than Mike?
Answer by ikleyn(52797) About Me  (Show Source):
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The ratio of Tom’s age to Mike’s age is 8:5.
30 years later, this ratio will be 6:5. How much older is Tom than Mike?
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Today, they are 8x (Tom) and 5x (Mike) years old, where x is the common measure of their ages.


30 years later

    %288x%2B30%29%2F%285x%2B30%29 = 6%2F5.


Cross-multiply, then simplify and find x

    5*(8x+30) = 6*(5x+30)

    40x + 150 = 30x + 180

    40x - 30x = 180 - 150

        10x   =     30

          x   =     30/10 = 3.


Hence, Tom is 8x = 8*3 = 24 yers old;  Mike is 5*3 = 15 years old.


Tom is  24-15 = 9 years older than Mike.    ANSWER

Solved.