Section 4 5 Solving Word Problems Using Systems

Example Strongsville High School is holding their annual musical. 650 tickets were sold for a value of $4375. If adult tickets cost $7. 50 and student tickets cost $3. 50, how many of each kind of ticket were sold? 1. Understand the problem. Let x = the number of adult tickets sold. Let y = the number of student tickets sold. 2. Write the first equation. Adult tickets + Student tickets = x + y = Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Total number sold 650 Continued 2

Example (cont) Strongsville High School is holding their annual musical. 650 tickets were sold for a value of $4375. If adult tickets cost $7. 50 and student tickets cost $3. 50, how many of each kind of ticket were sold? 2. Write the second equation. Value × number of adult tickets + Value × number of student tickets = Total value of all tickets sold 7. 5 x + 3. 5 y = 4375 We now have a system of equations. x+ y = 650 7. 5 x + 3. 5 y = 4375 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Continued 3

Example (cont) x+ y = 650 7. 5 x + 3. 5 y = 4375 3. Solve and state the answer. x = y + 650 7. 5( y + 650) + 3. 5 y = 4375 Solve equation (1) for x. Substitute the expression into (2). 7. 5 y + 4875 + 3. 5 y = 4375 y = 125 x + 125 = 650 x = 525 Substitute y = 125 into equation (1). The solution is (525, 125). Continued Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 4

Example (cont) x+ y = 650 7. 5 x + 3. 5 y = 4375 The solution is (525, 125). There were 525 adult tickets and 125 student tickets sold. 4. Check. 525 + 125 = 650 7. 5(525) + 3. 5(125) = 4375 3937. 5 + 437. 5 = 4375 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 5

Example A candy company wants to produce 20 pounds of chocolate with 45% fat content. To obtain this, a 50% fat content chocolate is combined with a 30% fat content chocolate. How many pounds of the 50% fat content chocolate and how many pounds of the 30% fat content chocolate should be used to make the desired 20 pounds? 1. Understand the problem. Let x = the number of pounds of chocolate of 50% fat content. Let y = the number of pounds of chocolate of 30% fat content. 2. Write the first equation. Lbs of 50% + Lbs of 30% = x + y = Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Total number of Lbs 20 Continued 6

Example (cont) A candy company wants to produce 20 pounds of chocolate with 45% fat content. To obtain this, a 50% fat content chocolate is combined with a 30% fat content chocolate. How many pounds of the 50% fat content chocolate and how many pounds of the 30% fat content chocolate should be used to make the desired 20 pounds? 2. Write the second equation. Percentage of fat × + Percentage of fat × lbs = lbs of 50% candy of 30% candy 0. 3 y + We now have a system of equations. x+ y = 20 0. 5 x + 0. 3 y = 9 0. 5 x = Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Percentage of fat × lbs of 45% candy . 45(20) Continued 7

Example (cont) x+ y = 20 0. 5 x + 0. 3 y = 9 3. Solve and state the answer. x = y + 20 0. 5( y +20) + 0. 3 y = 9 Solve equation (1) for x. Substitute the expression into equation (2). 0. 5 y + 10 + 0. 3 y = 9 y=5 Simplify. x + 5 = 20 x = 15 Substitute y = 5 into equation (1). The solution is (15, 5). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Continued 8

Example (cont) x+ y = 20 0. 5 x + 0. 3 y = 9 The solution is (15, 5). The candy company should use 15 pounds of 50% fat content chocolate and 5 pounds of 30% fat content chocolate. 4. Check. 15 + 5 = 20 20 = 20 0. 5(15) + 0. 3(5) = 9 7. 5 + 1. 5 = 9 9=9 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 9