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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblem 9
Chapter 6, Problem 9

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.
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Step 1: Define variables for the dimensions of the table tennis top. Let \(L\) represent the length and \(W\) represent the width.
Step 2: Write an equation for the perimeter of the rectangle. The perimeter \(P\) is given by \(P = 2L + 2W\). Since the perimeter is 28 feet, write the equation as \(2L + 2W = 28\).
Step 3: Write an equation for the difference between 4 times the length and 3 times the width. This is given as \(4L - 3W = 21\).
Step 4: Solve the system of equations formed by the two equations: \(2L + 2W = 28\) and \(4L - 3W = 21\). You can use substitution or elimination methods to find \(L\) and \(W\).
Step 5: After solving the system, interpret the values of \(L\) and \(W\) as the length and width of the table tennis top, respectively.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around the shape, calculated as 2 times the sum of its length and width (P = 2(L + W)). This formula helps relate the dimensions of the table tennis top to the given perimeter value.

Forming and Solving Systems of Linear Equations

When given multiple conditions involving length and width, we can form a system of linear equations. Solving these equations simultaneously allows us to find the exact dimensions that satisfy all conditions.
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Algebraic Manipulation and Substitution

Algebraic manipulation involves rearranging equations and substituting expressions to isolate variables. This technique is essential for solving the system of equations efficiently and finding the values of length and width.
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