SOLUTION: A rectangular pool is x feet by (x + 10) feet. A walkway that is 3 feet wide is placed completely around the pool forming a larger rectangle. The area of the rectangle formed by th

Algebra ->  Surface-area -> SOLUTION: A rectangular pool is x feet by (x + 10) feet. A walkway that is 3 feet wide is placed completely around the pool forming a larger rectangle. The area of the rectangle formed by th      Log On


   

Question 1041849: A rectangular pool is x feet by (x + 10) feet. A walkway that is 3 feet wide is placed completely around the pool forming a larger rectangle. The area of the rectangle formed by the pool and walkway is 192 square feet greater than the area of the pool alone. What is the area of the pool, in square feet?
Answer: 144 sq feet (How?)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = the area of the pool in ft2
(1) +A+=+x%2A%28+x%2B10+%29+
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You have to add 3 ft to both ends of the
width AND the length, so
Width of pool + walkway = +x+%2B+2%2A3+=+x+%2B+6+
Length of pool + walkway = +x+%2B+10+%2B+6+=+x+%2B+16+
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(2) +A+%2B+192+=+%28+x+%2B+6+%29%2A%28+x+%2B+16+%29+
Substitute (1) into (2)
(2) +x%2A%28+x+%2B+10+%29+%2B+192+=+%28+x+%2B+6+%29%2A%28+x+%2B+16+%29+
(2) +x%5E2+%2B+10x+%2B+192+=+x%5E2+%2B+22x+%2B+96+
(2) +10x+%2B+192+=+22x+%2B+96+
(2) +12x+=+96+
(2) +x+=+8+
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(1) +A+=+x%2A%28+x%2B10+%29+
(1) +A+=+8%2A%28+8%2B10+%29+
(1) +A+=+144+
the area of the pool is 144 ft2