Question

three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively they and up to 74 find these number​

Answer 1

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

According to question,

$\mathsf{ \implies x \: \cdot \: 2 \: + \: ( \: x \: + \: 1 )2 \: + \: ( \: x \: + \: 2 \: )4 \: = \: 74}$

$\mathsf{ \implies 2x \: + \: 2x \: + \: 2 \: + \: 4x \: + \: 8 \: = \: 74 }$

$\mathsf{\implies 8x \: + \: 10 \: = \: 74 }$

$\mathsf {\implies 8x \: = \: 74 \: - \: 10 }$

$\mathsf{\implies 8x \: = \: 64}$

$\mathsf{\implies x \: = \: \dfrac{64}{8}}$

$\mathsf {\therefore \quad \: x = \: 8}$

Henceforth, numbers are :

$\mathsf{= x, \: x \: + \: 1 , \: x \: + \:2 }$

$\mathsf{ =8, \: 8 \: + \: 1, \: 8 \: + \: 2 }$

$\mathsf{= 8, \: 9, \: 10}$

Answer 2

Step-by-step explanation:

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

So,

Integers are 7,8,9

Verification:

Hence the calculate integers are correct.

Hope it helps you.