Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

# 8.Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add up to 74. Find these numbers.

Let the three consecutive integers be x, x + 1 and x + 2.
As per the condition given, we have

2x + 3(x + 1) + 4(x + 2) = 74

$$\Rightarrow$$ 2x + 3x + 3 + 4x + 8 = 74

$$\Rightarrow$$ 9x + 11 = 74

$$\Rightarrow$$ 9x = 74 – 11 (transposing 11 to RHS)

$$\Rightarrow$$ 9x = 63

$$\Rightarrow$$ x = 63 ÷ 9 (transposing 9 to RHS)

$$\Rightarrow$$ x = 7

Thus, the required numbers are 7, 7 + 1 = 8 and 7 + 2 = 9, i.e., 7, 8 and 9.