1 ASSIGNMENT 1 Writing Systems

NAME______period______PAP ASSIGNMENT #1 ALGEBRA II Unit 2-1 Three Variable Systems WRITE THE SYSTEMS 1. ______and______Karen bought some 5 neon fish and 3 angel fish at $7.50 for her new aquarium. Then Karen bought 2 neon fish and 7 angel fish and spent $10.21. Write the system of equations to determine how much she spent on each type of fish.

2. ______and______Games ETC. charges $6 entrance fees plus $5 per hour to play games. GameTech charges a $10 entrance fee and $3 per hour to play games. Write system of equations will determine for what number of hours the same cost of playing games is the same for both companies.

3. ______and______Tom bought 11 student tickets to the football game and the 4 adult tickets for $35. Renee bought 5 student tickets and 7 adult tickets for $48. Write the system of equations that will determine the cost of adult tickets and the student tickets that they bought.

4. ______and______There were 42 people, teachers and students, in the Christmas play. There were five times as many students as teachers. Write the system of equations that could be used to find the number of teachers, t, and the number of students, s, in the play.

5. ______and______Your teacher gives you a test worth 100 points with 40 questions. Each question is worth either 2 points(x) or 4 points(y). Write a system of equations to determine the number of 2 point and 4 point questions on the test.

6. ______and______Kerry asked a bank teller to cash a $390 check using $20 and $50 bills. If the teller gave her a total of 15 bills, write a system of equations to determine how many of each type of bill she was given.

______7.The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters? A. l = w + 3; 2(l + w) = 85 B. l = 3w; 2l + 6w = 85 C. l = 3w; 2(l + w) = 85 D. l = w + 3; 2l + 6w = 85 NAME______period______PAP ASSIGNMENT #1 ______8.At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk? A. t + m = 2.10; 2t + 2m = 5.15 B. t + m = 2.10; 3t + 3m = 5.15. C. t + m = 2.10; 3t + 2m = 5.15 D. t + m = 2.10; 2t + 3m = 5.15.

______9.Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 108 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week? A. l + t = 108; t = 3l + 6 B. l + t = 108; t = 3l - 6 C. l + t = 108; l = 3t – 6 D. l + t = 108; l = 3t + 6

______10.The 1st truck traveled 406 miles in one month with twice the miles in the city, c, than on the highway, h. The 2nd truck traveled 5 more than 3 times the number of miles in the city than on the highway, which system of linear equations can be used to determine the number of miles travel on the highway & in the city? A. 2c + h = 406; 3c + 5 = h B: 3c + 5 = 406; 2c + 5 = h C. 2c + h = 406; 3h + 5 = c D. 2c = h; 3c + 5 = 406

11.An ice cream stand sells chocolate, vanilla, and strawberry ice cream. Yesterday, they sold a total of 232 ice cream sundaes. They sold 4 fewer than 3 times as many vanilla ice cream sundaes as strawberry. Strawberry and vanilla ice cream sundaes combined was equal to the number of chocolate ice cream sundaes sold.

Which system of equations models this situation? v + s + c = 232 v + s + c = 4 A) C) 3v - 4 = s 3s - 4 = v v – s = c v + c = s

v + s + c = 232 v + s + c = 116 B) D) 3s - 4 = v 3s - 4 = c v + s = c v +c = s NAME______period______PAP ASSIGNMENT #1

12.Eva had a bake sale to earn extra money. On the first day, she earned$6.25 selling 5 cookies and 2 brownies. On the second day, she earned $7.75 selling 3 brownies and 4 pieces of pie. On the third day, she earned $6.00 selling 8 cookies. If Eva sold 6 cookies and 1 piece of pie the next day, how much did she make?

A. $1.75 B. $2.45 C. $5.50 D. $6.75

13.A tool production company placed three orders for materials. The first order was for 13 generator pumps, 4 bundles of sheet metal, and 8 pair of safety glasses that cost a total of $543. The second order was for 6 generator pumps, 2 bundles of sheet metal, and 4 pair or safety glasses, and totaled $260. The third order was for 8 generator pumps, 3 bundles of sheet metal, and 5 pair of safety glasses with a total of $360. The bills do not list the per-item price. What are the costs of one bundle of sheet metal and one pair of safety glasses?

A. Bundles of sheet metal cost $23 each; safety glasses cost $7 each. B. Bundles of sheet metal cost $47 each; safety glasses cost $14 each. C. Bundles of sheet metal cost $23 each; safety glasses cost $15 each. D. Bundles of sheet metal cost $47 each; safety glasses cost $7 each.

14.A college entrance test has 112 questions. The test consists of true/false questions worth 7 points each, fill-in- the blank questions worth 9 points each and multiple- choice questions are worth 13 points each. There are 1172 possible points on the test. The number of multiple choice questions is 20 more than the number of true/false questions and the number of fill- in-the blank questions is 34 less that the number of true/false questions. How many points total on the test come from fill- in-the blank questions?

A) 42 B) 56 C) 72 D)104

15.Elise is an architect who is determining the dimensions of room with a rectangular floor plan in a building she is designing. The length measures 6 feet more than the width while the height is 8 feet less than the length. The total sum of the three measurements is 46. What are the length, width and height measurements of the room?

A) The length is 14ft., the width is 20ft., and the height is 12ft. B) The length is 20ft., the width is 12ft., and the height is 14ft. C) The length is 20ft., the width is 14ft., and the height is 12ft. NAME______period______PAP ASSIGNMENT #1 D) The length is 22ft., the width is 16ft., and the height is 14ft.

16.The concession stand at a movie theatre sells popcorn in small medium, and large containers. The prices are shown below. Popcorn Small………….$4.75 Medium……………$6.50 Large…………..$8.25

Yesterday, a total of 77 containers of popcorn were sold. Twice as many medium containers were sold as small containers. The concession stand collected a total of $555.25 from popcorn sales.

a) Write a system of three equations in three variables to describe the situation. Be sure to define any variables used.

b) Solve the system using matrix:

c) Describe the solution:

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