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Example 5.22 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution
Solve Systems of Equations by Substitution: example 5.22
The perimeter of a rectangle is 88. The length is five more than twice the width. Find the length and the width.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what you are looking for. We are looking for the length and width. Step 3. Name what we are looking for. Let the length
the widthStep 4. Translate into a system of equations. The perimeter of a rectangle is 88. 2L + 2W = P The length is five more than twice the width. The system is: Step 5. Solve the system of equations.
We will use substitution since the second
equation is solved for L.
Substitute 2W + 5 for L in the first equation.Solve for W. Substitute W = 13 into the second
equation and then solve for L.Step 6. Check the answer in the problem. Does a rectangle with length 31 and width
13 have perimeter 88? Yes.Step 7. Answer the equation. The length is 31 and the width is 13.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length and width of the rectangle.
How did it go?