Question

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

Answer 1

Solution :-

Let the three consecutive integers be (x), (x + 1) and (x + 2)

Now, according to the question.

(3*x) + 5*(x + 1) + 7*(x + 2) = 124

⇒ 3x + 5x + 5 + 7x + 14 = 124

⇒ 15x + 19 = 124

⇒ 15x = 124 - 19

⇒ 15x = 105

⇒ x = 105/7

⇒ x = 7

Now, the consecutive integers are 7, 7 + 1 = 8 and 7 + 2 = 9

Three consecutive integers  are 7, 8 and 9

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

21 + (5*8) + (7*9) = 124

21 + 40 + 63 = 124

124 = 124

LHS = RHS

Answer