Question

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Answer 1

Let, the integers be,

x , x+1 and x+2 {since they are consecutive}

A/Q:-

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

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

9x + 11 = 74

9x = 74-11

9x = 63

x = 7

The numbers are 7, (7+1 = )8 , (7+2=)9.

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Answer 2

Question:

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

Solution:

Given three consecutive integers taken in an increasing order and multiplied by 2, 3 and 4 respectively and add up to 74.

Let the three consecutive integers be $x$, $x+1$ and $x+2$.

So, the equation is $2(x)+3(x+1)+4(x+2)=74$

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

$9x+11=74$

$9x=74-11$

$9x=63$

$x=\frac{63}{9}$

$x=7$

So,

$x=7$

$x+1=8$

$x+2=9$

Therefore, the three consecutive integers add up to give 74 when they are taken in an increasing order and multiplied by 2, 3 and 4 respectively are 7, 8 and 9.