Question

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

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.