Question

The product of two integers is 72. One number is two less than five times the other.

Which of the following equations could be used to find one of the numbers?

Answer 1

Equation is 5x² - 2x - 72 = 0 and the two integers are 4 and 18

Explanation:

• Step 1: Let one number be x. Then the other is 5x - 2. Product = 72

⇒ 72 = x(5x - 2)

⇒ 72 = 5x² - 2x

⇒ 5x² - 2x - 72 = 0 is the equation

x = 2 ± √4 - 4 × 5 × -72/2 × 5 (Using quadratic formula)

x = 2 ± √4 + 1440/10

x = 2 ± 38/10

= 40/10, -36/10 (negative decimal value is neglected)

∴ x = 4

5x - 2 = 20 - 2 = 18