Loading…
Example 5.41 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.41
Translate to a system of equations and then solve:
Randall has 125 feet of fencing to enclose the rectangular part of his backyard adjacent to his house. He will only need to fence around three sides, because the fourth side will be the wall of the house. He wants the length of the fenced yard (parallel to the house wall) to be 5 feet more than four times as long as 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 of the fenced yard.
the width of the fenced yardStep 4. Translate into a system of equations. One length and two widths equal 125. The length will be 5 feet more than four times the width. The system is:
Step 5. Solve the system of equations by substitution.Substitute L = 4W + 5 into the first
equation, then solve for W.Substitute 20 for W in the second
equation, then solve for L.Step 6. Check the answer in the problem. Step 7. Answer the equation. The length is 85 feet and the width is 20 feet.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and then solve:
Mario wants to put a rectangular fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There are two long sides and the one shorter side is parallel to the house. He needs 155 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.
How did it go?