SOLUTION: Pat's present age is three-fourths of Ken's present age. In 15 years the sum of their ages will be 58, Find their present ages.

Question 176551: Pat's present age is three-fourths of Ken's present age. In 15 years the sum of their ages will be 58, Find their present ages.
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = pat's present age.
let y = ken's present age.
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Pat's present age is three-fourths of Ken's present age.
x = 3/4 * y
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In 15 years the sum of their ages will be 58
x + 15 + y + 15 = 58
combine like terms to get:
x + y + 30 = 58
subtract 30 from both sides of equation to get:
x + y = 28
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substitute 3/4 * y for x to get:
3/4 * y + y = 28
multiply both sides of equation by 4 to get:
3*y + 4*y = 4*28
combine like terms to get:
7*y = 4*28
divide both sides of equation by 7 to get:
y = 4*28/7
simplify to get:
y = 16
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since x = 3/4*y, then:
x = (3/4)*16 = 3*16/4 = 3*4 = 12
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you have:
x = 12
y = 16
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pat is 12
ken is 16
pat's age is 3/4 * ken's age.
in 15 years, pat will be 27 and ken will be 31.
sum of their ages will be 58
everything checks out.
answer is:
pat is 12
ken is 16
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