EXAMPLE 2 Write a system of equations, and solve. In-Class Example 2 Martha wants to put a fence around her rectangular garden. It is 4 ft longer than it is wide. If she needs 28 ft of fencing, find the dimensions of the garden. Answer: 5 ft 9 ft l w 2 Solve Geometry Problems A builder installed a rectangular window in a new house and needs 182 in. of trim to go around it on the inside of the house. Find the dimensions of the window if the width is 23 in. less than the length. Solution Step 1: Read the problem carefully, and identify what we are being asked to fi nd. Draw a picture. We must fi nd the length and width of the window. Step 2: Choose variables to represent the unknown quantities. w the width of the window l the length of the window Label the picture with the variables. Step 3: Write a system of equations using two variables. To get one equation, we know that the width is 23 in. less than the length. We can write the equation w l 23. If it takes 182 in. of trim to go around the window, this is the perimeter of the rectangular window. Use the equation for the perimeter of a rectangle. 2l 2w 182 The system of equations is w l 23 2l 2w 182. Step 4: Solve the system. 2l 2w 182 2l 2(l 23) 182 Substitute. 2l 2l 46 182 Distribute. 4l 46 182 Combine like terms. 4l 228 Add 46 to each side. 4 l 4 l 57 Simplify. Find w by substituting l 57 into w l 23. w 57 23 34 The solution to the system is (57, 34). (The ordered pair is written as (l, w), in alphabetical order.) Step 5: Check the answer, and interpret the solution as it relates to the problem. The length of the window is 57 in., and the width is 34 in. The check is left to the student. YOU TRY 2 Write a system of equations and solve. 228 4 Divide each side by 4. The top of a desk is twice as long as it is wide. If the perimeter of the desk is 162 in., fi nd its dimensions. 276 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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