A fence must go around a rectangular swimming pool whose perimeter is 150 feet. The pool's length is 15 feet more than its width. What are the pool's dimensions?

1. Let W stand for the width in feet, so the length is W plus 15. 2. The perimeter of a rectangle is twice the length plus twice the width: 2(W plus 15) plus 2W equals 150. 3. Distribute: 2W plus 30 plus 2W equals 150. 4. Combine like terms: 4W plus 30 equals 150. 5. Subtract 30 and divide by 4: 4W equals 120, so W equals 30 feet, and the length is 30 plus 15, which is 45 feet. 6. Check both conditions: 2(45) plus 2(30) equals 90 plus 60, which is 150 feet, and 45 is exactly 15 more than 30. 7. 50 by 25 also gives a 150-foot perimeter, but 50 is 25 more than 25, so it fails the 15-feet-more condition. 8. 40 by 35 matches the perimeter too, yet the sides differ by only 5 feet, so it fails the same condition. 9. 60 by 15 keeps the perimeter but makes the length 45 feet more than the width, which is far past the stated 15. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.4 Use Properties of Rectangles, Triangles, and Trapezoids_