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.
