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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
⇒ 𝑥2 + 𝑥 - 30 = 0
⇒ 𝑥2 + 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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