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messersmith_power_introductory_algebra_1e_ch4_7_10

Step 4: Solve the system. Use the elimination method. Multiply the fi rst equation by 2 to eliminate x. 4x 8y 704   4x 3y 609 5y 95 Add the equations. y 19 Find x. We will substitute y 19 into 2x 4y 352. 2x 4(19) 352 Substitute. 2x 76 352 Multiply. 2x 276 Subtract 76 from each side. x 138 The solution to the system is (138, 19). Step 5: Check the answer, and interpret the solution as it relates to the problem. A Broadway play ticket costs $138.00, and a ticket to the top of the Empire State Building costs $19.00. The check is left to the student. YOU TRY 3 Write a system of equations, and solve. Torie bought three scarves and a belt for $105 while Liz bought two scarves and two belts for $98. Find the cost of a scarf and a belt. In Chapter 2, we learned how to solve mixture problems by writing an equation in one variable. Now we will learn how to solve the same type of problem using two variables and a system of equations. 4 Solve Mixture Problems EXAMPLE 4 In-Class Example 4 How many ounces of a 6% alcohol solution and how many ounces of an 18% alcohol solution should be mixed to make 50 oz of a 10% alcohol solution? Answer: 6%: 33 1 3 oz; 18%: 16 2 3 oz A pharmacist needs to make 200 mL of a 10% hydrogen peroxide solution. She will make it from some 8% hydrogen peroxide solution and some 16% hydrogen peroxide solution that are in the storeroom. How much of the 8% solution and 16% solution should she use? 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 amount of 8% solution and 16% solution she should use. A ount o solution x A ount o solution y 2 o solution Remember that a hydrogen peroxide solution contains both pure hydrogen peroxide and pure water. 278 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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