Question

Consider three consecutive odd integers. The ratio of the smallest number to one less than twice the smallest

number is equivalent to the ratio of three more than the middle number to twice the largest number. What are
the three integers?

Answer 1

Let x be the smallest of the three integers. Then the next two are x + 2 and x + 4.

• "The ratio of the smallest number to 1 less than twice the smallest number..."

This translates to

x / (2x - 1)

• "... the ratio of 3 more than the middle number to twice the largest number."

This translates to

((x + 2) + 3) / (2 (x + 4))

or, simplifying a bit,

(x + 5) / (2x + 8)

The ratioes are said to be equivalent, so

x / (2x - 1) = (x + 5) / (2x + 8)

Solve for x :

x (2x + 8) = (x + 5) (2x - 1)

2x² + 8x = 2x² + 9x - 5

8x = 9x - 5

-x = -5

x = 5

So the three integers are 5, 7, and 9.