Question

When the smallest of three consecutive odd integers is added to four times the largest, it produces a result 729 more than four times the middle integer. Find the numbers and check your answer.

Answer 1

Let the integers be represented by x, x+2 and x + 4.

Then,

x + 4(x+4) = 729 + 4(x+2)

So,

x + 4x + 16 = 729 + 4x + 8

So,

x = 721.

So,

the numbers are:

721, 723, 725

CHECK:

smallest = 721

Four times the largest = 4 X 725 = 2900

These two are added.

Thus, we get:

721 + 2900 = 3621         (1)

Four times the middle integer = 4 X 723 = 2892

729 more than the above number = 729 + 2892 = 3621                (2)
(1) & (2) both are = 3621.

So, this is checked.