Adam is building a rectangular swimming pool. The perimeter of the pool must be no more than 120 feet. If the length of the pool is 22 feet, write and solve an inequality that represents what the width of the pool must be.
Let's let the width of the pool be represented by the variable "w".
The perimeter of the pool can be calculated as P = 2l + 2w, where l is the length and w is the width.
Substituting the given values: 120 = 2(22) + 2w
Simplifying: 120 = 44 + 2w
Subtracting 44 from both sides: 76 = 2w
Dividing both sides by 2: 38 = w
Therefore, the width of the pool must be no more than 38 feet.
Let's start by assigning a variable to represent the width of the pool. Let's use the letter 'w' for width.
According to the problem, the length of the pool is given as 22 feet, and the perimeter of the pool must be no more than 120 feet.
The formula for the perimeter of a rectangle is given by P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Substituting the given values into the formula, we get:
120 ≤ 2(22) + 2W
Simplifying the equation, we have:
120 ≤ 44 + 2W
Now, let's isolate the variable W by subtracting 44 from both sides of the inequality:
120 - 44 ≤ 44 + 2W - 44
76 ≤ 2W
Finally, divide both sides of the inequality by 2 to solve for W:
76/2 ≤ 2W/2
38 ≤ W
Therefore, the inequality that represents the width of the pool is W ≥ 38 feet.