Math Chapter 7 Story Problems Solutions

Algebra 1 CP Chapter 7: Systems - Story Problems Notes Methods for solving story problems: 1. Read the problem through entirely. 2. Define your variable(s). Look at the question at the end to help define the variables. 3. Read the problem again and construct the two equations. **EXAMPLE 1** Lorena bought 10 packs of Styrofoam cups for the graduation dance. A pack of 12-oz cups costs $1.80 and a pack of 16-oz cups costs $2.40. Lorena paid a total of $21.60 excluding tax. How many packs of each did she buy? x = packs   of 12 oz cups y = packs of 16 oz cups x + y = 10 → y = -x + 10 1.80x + 2.40y = 21.60 1.80x + 2.40(-x + 10) = 21.60 1.80x - 2.40x + 24 = 21.60 -0.60x + 24 = 21.60 -0.60x = -2.40 x = 4, y = 6 **EXAMPLE 2** The table below shows the ticket sales at an all-age comedy club on a Friday and a Saturday night. | Day | Number of adult tickets | Number of student tickets | Total sales (in dollars) | |---|---|---|---| | Friday | 30 | 20 | 910 | | Saturday | 50 | 30 | 1475 | Find the cost of an adult ticket and the price of a student ticket.   x = cost of adult ticket y = price of student ticket 3(30x + 20y = 910) -2(50x + 30y = 1475) 90x + 60y = 2730 -100x - 60y = -2950 ------------------- -10x = -220 x = 22 y = 4.50 **EXAMPLE 3** There are sixteen workers employed on a highway project, some at $200 per day and some at $165 per day. The daily payroll is $2745. Find the number of workers employed at each   wage. x = # of $200 workers = 3 y = # of $165 workers = 13 x + y = 16 200x + 165y = 2745 EXAMPLE 4 A store sold 28 pairs of cross-trainer shoes for a total of $2220. Style A sold for $70 and style B sold for $90. How many of each were sold?   x = # of style A y = # of style B x + y = 28 70x + 90y = 2220 EXAMPLE 5 A Chinese restaurant offers two sizes of dishes: Queen and King. All Queen dishes cost the same and all King dishes cost the same. One person buys 3 Queen dishes and 5 King dishes and the bill came to $28.20. Another person buys 4 Queen dishes and 3 King dishes and the total came to $23.30. What is the cost of each dish?   x = cost of Q y = cost of K 3x + 5y = 28.20 4x + 3y = 23.30