SYSTEMS OF EQUATIONS WORD PROBLEMS

OPENING ACTIVITY (COMPLETE WITH A PARTNER) You and your friend each purchased identical subscriptions to an online video rental site. When you joined, you each paid the one-time membership processing fee. You also paid a flat rate for each movie that you downloaded. By the end of the first month, you had downloaded 8 movies and paid $16.50, Your friend had downloaded only 6 movies and paid $14.00. Find the following: What was the one-time membership fee? What is the per-movie rental fee?

OPENING ACTIVITY Define your variables (What are you looking for?) You and your friend each purchased identical subscriptions to an online video rental site. When you joined, you each paid the one-time membership processing fee. You also paid a flat rate for each movie that you downloaded. By the end of the first month, you had downloaded 8 movies and paid $16.50, Your friend had downloaded only 6 movies and paid $14.00. Find the following: What was the one-time membership fee? What is the per-movie rental fee? Define your variables (What are you looking for?) r = membership rate m = movie price

OPENING ACTIVITY Define your variables (What are you looking for?) By the end of the first month, you had downloaded 8 movies and paid $16.50, Your friend had downloaded only 6 movies and paid $14.00. Define your variables (What are you looking for?) r = membership rate m = movie price Set up an equation for your total cost and your friend’s total cost Your cost  8m + r = 16.50 Friend’s cost  6m + r = 14.00

OPENING ACTIVITY 3. Solve by elimination! Solve your system of equations by using an appropriate method (we will use elimination in this example) 3. Solve by elimination! Your cost  8m + r = 16.50 Friend’s cost  -(6m + r = 14.00) 2m = 2.5 m = 1.25 Find r by substitution! 8(1.25) + r = 16.50 10 + r = 16.50 r = 6.50 Membership rate = $6.50 Cost per movie = $1.25

ACTIVITY 2 (COMPLETE WITH A PARTNER) Tyler and Caleb go to Yummy Donuts to get treats for their friends. Tyler buys 5 donuts and 3 cups of coffee and spends $6. Caleb buys 3 donuts and 6 cups of coffee and spends $8.85. What is the price for one donut and one cup of coffee?

ACTIVITY 2 Tyler and Caleb go to Yummy Donuts to get treats for their friends. Tyler buys 5 donuts and 3 cups of coffee and spends $6. Caleb buys 3 donuts and 6 cups of coffee and spends $8.85. What is the price for one donut and one cup of coffee? Define your variables (What are you looking for?) d = price of a donut c = price of a cup of coffee Set up an equation for Tyler’s total cost and Caleb’s total cost Tyler’s cost  5d + 3c = 6.00 Caleb’s cost  3d + 6c = 8.85

ACTIVITY 2 3. Solve by elimination! Solve your system of equations by using an appropriate method (we will use elimination in this example) 3. Solve by elimination! Tyler’s cost  5d + 3c = 6.00 2(5d + 3c = 6.00) Caleb’s cost  3d + 6c = 8.85 7d = 3.15 d = 0.45 Find c by substitution! 5(0.45) + 3c = 6.00 2.25 + 3c = 6.00 3c = 3.75 c = 1.25 10d + 6c =12.00 -(3d + 6c = 8.85) Cost per donut = $0.45 Cost per coffee = $1.25

ACTIVITY 3 (COMPLETE WITH A PARTNER) You and your friend Jim are buying snacks for the Spanish Fiesta. You buy 2 bags of nachos and 1 jar of salsa and spend $8.90. Jim buys 4 bags of nachos and 3 jars of salsa and spends $19.70. What is the price for one bag of nachos and one jar of salsa? Define the variables you need to solve this problem. Set up equations representing the total costs for your purchase and Jim’s purchase. Solve your system of equations.

ACTIVITY 3 Define your variables Set up equations n = price of a bag of nachos s = price of a jar of salsa Set up equations Your cost  2n + s = 8.90 Jim’s cost  4n + 3s = 19.70 Solve by elimination! Your cost  3(2n + s = 8.90) Jim’s cost  4n + 3s = 19.70 6n + 3s = 26.70 -(4n + 3s = 19.70) 2n = 7.00 n = 3.50 Find s by substitution! 2(3.50) + s = 8.90 7 + s = 8.90 s = 1.90 Cost per bag of nachos = $3.50 Cost per jar of salsa = $1.90

TRY ONE ON YOUR OWN! Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 shirts, how many of each kind did she buy?

TRY ONE ON YOUR OWN! Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 shirts, how many of each kind did she buy? 1. Define your variables. f = number of fancy shirts p = number of plain shirts 2. Set up your equations. Total number of shirts  f + p = 7 Cost of shirts  28f + 15p = 131 3. Solve by elimination! Total  15(f + p = 7) cost  28f + 15p = 131 Find p by substitution! 2 + p = 7 p = 5 15f + 15p = 105 -(28f + 15p = 131) -13f = -26 f = 2 2 fancy shirts 5 plain shirts