#### Question

Determine two consecutive multiples of 3, whose product is 270.

#### Solution

Let the two consecutive multiples of 3 are 3x and 3x + 3

Given that their product is 270

⇒ (3x) (3x + 3) = 270

⇒ x(3x + 3) = 90

⇒ 𝑥^{2} + 𝑥 - 30 = 0

⇒ 𝑥^{2} + 6𝑥 - 5𝑥 - 30 = 0

⇒ x(x + 6) - 5(x + 6) = 0

⇒ (x + 6) (x - 5) = 0

⇒ x = 5 or x = -6

Considering the positive value of x.

⇒ x = 5, 3x = 15 and 3x + 3 = 18

∴ The two consecutive multiples of 3 are 15 and 18.

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#### APPEARS IN

Solution Determine Two Consecutive Multiples of 3, Whose Product is 270. Concept: Solutions of Quadratic Equations by Factorization.