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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.

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Question:

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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