5.3: Applications of Systems of Linear Equations (AKA Word Problems) Algebra 2 5.3: Applications of Systems of Linear Equations (AKA Word Problems)

Problem 1 M = Y – 32.8 M + Y = 266.6 M = (149.7) – 32.8 In 2003, the New York Yankees and the New York Mets had the highest payrolls in major league baseball. The Mets’ payroll was $32.8 million less than the Yankees. If the two payrolls totaled $266.6 million, what was the payroll of each team? M = Y – 32.8 M = (149.7) – 32.8 M = 116.9 M + Y = 266.6 (Y – 32.8) + Y = 266.6 2Y – 32.8 = 266.6 2Y = 299.4 Y = 149.7 Mets = $116.9 million Yankees = $149.7 million

Problem 2 It was reported in 2004 that during the National Hockey League and National Basketball Association seasons, two hockey tickets and one basketball ticket cost $126.77. At the same prices, one hockey ticket and two basketball tickets cost $128.86. What were the average ticket prices for the two sports? (1) (-2) Hockey Ticket = $41.36 Basketball Ticket = $43.65

Problem 3 $6 x 6x $2 y 2y $5 200 5(200) Continued… Randall wants to mix a total of 200 lbs of nuts worth $5 per pound by mixing some $6 per pound cashews with some $2 per pound peanuts. How many pounds of each type of nut must he mix? Cost Pounds Total $6 x 6x $2 y 2y $5 200 5(200) Equation 1 Equation 2 Continued…

Problem 3 continued… (-6) (1) 150 pounds of cashews 50 pounds of peanuts

Problem 4 Carter Fenton invested $12,000 last year in two accounts: one earning 3% interest and the other earning 4%. If he made $440 in interest last year, how much did he have in each account? % Amount Invested Interest 3% x .03x 4% y .04y 12,000 440 Equation 1 Equation 2 Continued…

Problem 4 continued… (-.03) (1) $4,000 at 3% interest