Question

Tom is 26 years older than Paul. the product of his ages is 560. How old is Paul?

Answer 1

Given data:

The given age of Tom is T=P+26.

The expression for the product of their ages is TxP=560.

Substitute (P+26) for T in the second expression.

$\begin{gathered} (P+26)P=560 \\ P^2+26P-560=0 \\ P^2+40P-14P-560=0 \\ P(P+40)-14(P+40)=0 \\ (P+40)(P-14)=0 \\ P=-40,\text{ 14} \\ P=14 \end{gathered}$

Thus, the age of Paul is 14 years.