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1. The difference between two integers is 5. Their product is 500. Find the numbers.

A. 15, 20

B. 20, 25

C. 30, 25

D. 21, 26

Solution:

Let the integers be x and (x + 5)
Then,

\begin{aligned} \Leftrightarrow x (x + 5) = 500 \\ \Leftrightarrow x^{2} + 5 x - 500 = 0 \\ \Leftrightarrow (x + 25) (x - 20) = 0 \\ \Leftrightarrow x = 20 \end{aligned}

So, the numbers are 20 and 25

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