Question 1101201: A father is twice as old as his son. The product of their ages 10 years ago was 532,find the age of the father Now Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52754) (Show Source):
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A father is twice as old as his son. The product of their ages 10 years ago was 532,find the age of the father Now
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Let x be the son's age.
Then the father's age is 2x years.
The condition gives you an equation
(x-10)*(2x-10) = 532, or
2x^2 - 30x + 100 = 532,
2x^2 - 30x - 432 = 0,
x^2 - 15x - 216 = 0.
= = .
The only positive solution is x= 24.
Answer. The son is 24 years old. The father is 48 years old.
Check. (24-10)*(48-10) = 532. ! Correct !
You can also solve this problem without algebra by playing with the numbers.
10 years ago, the product of their ages was 532. So look for a pair of whole numbers whose product is 532 and which are reasonable for the ages of a father and his son.
532 = 133*4 definitely not reasonable
532 = 7*19*4 so maybe 19 and 28? no, not reasonable
532 = 19*28 = 38*14
Yes; that is promising. Does it meet the other requirements of the problem?
Those are supposed to be their ages 10 years ago, so their current ages would be 48 and 24.
And yes, that makes the father twice as old as his son.
