Problem 14 - Introductory Algebra for College Students

Question

The perimeter of a tennis court is 228 feet. After a round of tennis, a player's coach estimates that the athlete has run a total of 690 feet, which is equivalent to 7 times the court's length plus four times its width. What are the dimensions of a standard tennis court?

Step-by-Step Solution

Answer

The dimensions of the tennis court are 78 feet (length) and 36 feet (width)

Step 1 - Setting up equations

From the problem, 2 equations can be set up:1. The perimeter of a rectangle (tennis court in this case), which is given by \( 2\times length + 2\times width = Perimeter \). Since the perimeter is given as 228 feet, we can set up the equation as: \(2L + 2W = 228\)2. The total distance ran by the athlete, given as \( 7 \times length + 4\times width = Total Distance \). Since the total distance ran is given as 690 feet, we can set this equation up as: \(7L + 4W = 690\)

Step 2 - Solve the equations

To solve the equations, start by simplifying the perimeter equation by dividing by 2 to remove the common factor: \( L + W = 114 \).Then, isolate one of the variables in the simplified equation. For instance, isolate \( L \) by subtracting \( W \) from both sides: \( L = 114 - W \).Substitute \( L = 114 - W \) into the second equation \( 7L + 4W = 690 \) to get a new equation in terms of \( W \) only: \( 7(114 - W) + 4W = 690 \)

Step 3 - Solve for width

Solving the equation \( 7(114 - W) + 4W = 690 \) gives us the width (W) of the court.This simplifies to \( 798 - 7W + 4W = 690 \), which further simplifies to \( 3W = 108 \), and finally \( W = 36 \) feet.

Step 4 - Solve for length

Substitute \( W = 36 \) back into the equation \( L + W = 114 \) to find the length (L) of the court.This simplifies to \( L = 114 - 36 = 78 \) feet.