Question

Q1) 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 number.​

Answer 1

Answer:Three consecutive integers are 7,8 and 9

Solution:

Let the numbers are x, x+1 and x+2

(Since these are consecutive integers)

they are taken in increasing order and multiplied by 2,3 and 4 respectively

So x becomes 2x

(x+1) becomes 3(x+1)

(x+2) becomes 4(x+2)

they add up to 74,so ATQ

$2x + 3(x + 1) + 4(x + 2) = 74 \\ 2x + 3x + 3 + 4x + 8 = 74 \\ 9x + 11 = 74 \\ 9x = 74 - 11 \\ 9x = 63 \\ x = \frac{63}{9 } \\ x = 7$

So,

Integers are 7,8,9

Verification:

$2 \times 7 + 3 \times 8 + 4 \times 9 \\ = 14 + 24 + 36 \\ = 74$

Hence the calculate integers are correct.

Hope it helps you.

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