what is the pair of consecutive multiples of 3 that are natural both of which are larger 22 such that - Maths - Linear Inequalities

Question

what is the pair of consecutive multiples of 3 that are natural
both of which are larger 22 such that their sum is less than
60?

Ankush Jain · Accepted Answer

Let 3x be the smallest of two consecutive multiples of 3. Therefore, the other multiple is 3x + 3.

It is given that both the integers are larger than 22 and their sum is less than 60. Therefore,

3x > 22 and 3x + 3x + 3 < 60

⇒ x > $\frac{22}{3}$ and 6x < 57

⇒ x > $\frac{22}{3}$ and x < $\frac{19}{2}$

⇒ $\frac{22}{3}$ < x < $\frac{19}{2}$

⇒ x = 8, 9

Hence, the required pair of even integers are (24, 27) and (27, 30).

what is the pair of consecutive multiples of 3 that are natural both of which are larger 22 such that their sum is less than 60?