Here is a plan: 1) we express the length of the pool in terms of width and the length and width of the enclosure in terms of the width of the pool.
2)We write an equation expressing the area of the deck in terms of the total area of enclosure with pool minus the area of the pool, then solve for width.
3)Find the length of the pool and area of the pool.
Step 1. Length = 3 less than twice the width.
l = -3 +2w,
l = 2w - 3.
The width of the deck is 4 m. This means that the total length will be
lenclosure = l + 2•4,
lenclosure = 2w -3 +8 = 2w+5.
The same way,
wenclosure = w + 2•4 = w+8.
Adeck = Aenclosure - Apool
400 = (w+8)(2w+5) - w(2w-3),
400 = 2w2 +16w+5w+40 - 2w2 + 3w.
You can simplify and solve this equation and find that w=15 m.
Step 3. Length and area of the pool.
l = 2•15 -3 = 27 m.
The area of the pool is 405 square meters.
Interesting, the area of the pool is about the same as the area of the deck, only 5 square meters more.
Try it again. If you change the width of the deck to 3 m or 5 m, can you solve this modified problem?