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.
Percent increase find increase first 10500 to 11300 11300-10500=800 so percent increase change/original origianal=10500 change=800 800/10500=8/105=0.0761 percent means parts out of 100 0.0761/1 times 100/100=7.61/100=7.61%
