OK. I did it, and I have the solution. _____________________________________
The length of the deck is (5 + 2x) . The width of the deck is (4 + 2x) .
If the deck didn't have that big hole in the middle where the pool is, then its area would be
(5 + 2x) · (4 + 2x) .
When you multiply that all out, you get Area = 4x² + 18x + 20
and the question tells us that the area of the whole big rectangle is 90 yds² . So we can write
4x² + 18x + 20 = 90 .
Subtract 90 from each side: 4x² + 18x - 70 = 0 Divide each side by 2 : 2x² + 9x - 35 = 0
You can use the quadratic equation to solve that and find out that x = 2.5 yards, and that's what the question is asking you. ___________________________________________________
That makes the deck 10 yds high and 9 yds wide.
Total area of the whole big rectangle, (deck + pool ), = 90 yds².
The numbers are 5 and 12. Smaller number = x Larger number = y x +y =17 y = 3x - 3 x +3x -3 = 17 4x = 20 x = 5 smaller number is 5 y = 3(5) - 3 y = 12 larger number is 12.
