Question

The product of two successive integral multiples of 5 is 300. Determine the multiples.

Answer 1

Given that the product of two successive integral multiples of 5 is 300.

Let the integers be 5x, and 5(x + 1)

Then, by the integers be 5x and 5(x + 1)

Then, by the hypothesis, we have

5x ∙ 5(x + 1) = 300

⇒ 25x (x + 1) = 300

⇒ 𝑥² + 𝑥 = 12

⇒ 𝑥² + 𝑥 - 12 = 0

⇒ 𝑥² + 4𝑥 - 3𝑥 - 12 = 0

⇒ x(x + 4) -3(x + 4) = 0

⇒ (x + 4) (x – 3) = 0

⇒ x = -4 or x = 3

If x = -4, 5x = -20, 5(x + 1) = -15

x = 3, 5x = 15, 5(x + 1) = 20

∴ The two successive integral multiples are 15, 20 or -15, -20.