Question

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

Answer 1

Answer:

The numbers are 7,8,9 respectively.

Step-by-step explanation:

Let the three consecutive integers be :- x , x+1 , x+2

Multiplying by 2,3,4 respectively gives 2x , 3x+3 , 4x+8

Adding them gives 2x+3x+3+4x+8 = 9x + 11

Since this is 74,

9x = 74–11

9x = 63

x = 7

Therefore x=7  then the consecutive terms will be 8 & 9

The integers are 7, 8 and 9.

Answer 2

The numbers are consecutive so let the numbers be ⇒

$x,(x+1),(x+2)$

According to the question, they are taken in increasing order and multiplied by 2,3 and 4.

So the values change and now they are as follows.

$x\rightarrow 2x\\\\(x+1) \rightarrow 3\times (x+1)\\\\(x+2) \rightarrow 4\times (x+2)$

According to the question, these numbers sum up to 74. So our equation would be as follows.

$2x+3\times (x+1) + 4\times (x+2)=74$

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

$9x+11=74$

$9x=74-11$

$9x=63$

$x=63 \div 9$

$x= 7$

Verification

$2 \times 7 + 3 \times 8 + 4 \times 9$

$14 + 24 + 36$

$74$

∴ The integers are 7 (x), 8 (x+1 = 7+1), and 9 (x+2 = 7+2).