Question

the three consecutive integers are such that when they are taken in increasing order and multiplied by 3, 5 and 7 , they add up to 124. find these numbers.

Answer 1

Let the numbers be x, x+1, x+2
3x +5(x+1)+7(x+2)=124
3x+5x+5+7x+14=124
15x+19=124
15x=105
x=7
x+1=8
×+2=9
The three numbers are 7,8 and 9.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

$\textbf{\underline{Consecutive\; Intetgers}}$

p , p + 1 , p + 2

Hence,

Situation :-

(3 × p) + 5 × (p + 1) + 7 × (p + 2) = 124

3p + 5p + 5 + 7p + 14 = 124

15p + 19 = 124

15p = 124 - 19

15p = 105

$\tt{\rightarrow p=\dfrac{105}{7}}$

p = 7

Therefore,

$\textbf{\underline{Consecutive\; Intetgers}}$

7

7 + 1 = 8

7 + 2 = 9

$\textbf{\underline{3\; consecutive\; integers}}$

= 7 , 8 , 9

Now,

3 × 7 + 5 × (7 + 1) + 7 × (7 + 2) = 124

21 + (5 × 8) + (7 × 9) = 124

21 + 40 + 63 = 124

124 = 124

Hence we get :-

$\textbf{\underline{Left\;Hand\;side=Right\;hand\; side}}$