Determine two consecutive multiples of 3 whose product is 270.

1.	Determine two consecutive multiples of 3 whose product is 270.
Answer» Let the two consecutive multiples of 3 be 3x and 3x + 3 From the question, it’s given that 3x(3x + 3) = 270 ⇒ x(3x + 3) = 90 [Dividing by 3 both sides] ⇒ 3x²+ 3x = 90 ⇒ 3x²+ 3x – 90 = 0 ⇒ x²+ x – 30 = 0 Solving for x by factorization method, we have* x²+ 6x – 5x – 30 = 0 ⇒ x(x + 6) – 5(x + 6) = 0 ⇒ (x + 6)(x – 5) = 0 Now, either x + 6 = 0 ⇒ x = – 6 Or, x – 5 = 0 ⇒ x = 5 Considering the positive value of x, we have only x = 5, so 3x = 15 and 3x + 3 = 18. Thus, the two consecutive multiples of 3 are 15 and 18 respectively.

Answer»

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

From the question, it’s given that

3x*(3x + 3) = 270

⇒ x(3x + 3) = 90 [Dividing by 3 both sides]

⇒ 3x²+ 3x = 90

⇒ 3x²+ 3x – 90 = 0

⇒ x²+ x – 30 = 0

Solving for x by factorization method, we have

x²+ 6x – 5x – 30 = 0

⇒ x(x + 6) – 5(x + 6) = 0

⇒ (x + 6)(x – 5) = 0

Now, either x + 6 = 0 ⇒ x = – 6

Or, x – 5 = 0 ⇒ x = 5

Considering the positive value of x, we have only

x = 5, so 3x = 15 and 3x + 3 = 18.

Thus, the two consecutive multiples of 3 are 15 and 18 respectively.

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