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Question:
Sam is now 5 times as old as his son Paul. Four years ago, the product of their ages was 52. Find their present ages.
A
Sam: 30 years; Paul: 6 years.
explanation
Note: Remember that the term product means the result of multiplying two numbers and sum is the result of addition.
Let x be the age of Paul
5x = the age of Sam
x - 4 = the age of Paul 4 years ago
5x - 4 = the age of Sam 4 years ago
(x−4)(5x−4)=52
\(5x^2-20x-4x+16=52\)
\(5x^2-24x-36=0\)
(5x+6)(x−6)=0
5x+6=0 and x−6=0
5x+6=0 will yield a negative value for x, so this is not possible solution.
x−6=0
x=6 : the age of Paul
5x=5(6)=30 : the age of Sam
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