Writing a System of Equations from a Context

A large pizza at one local restaurant sells for $9 plus $0.50 per topping. A large pizza at another restaurant sells for $12 plus $0.25 per topping. What system of equations can be used to find the number of toppings when both companies cost the same amount?

• y = 0.25x + 9

  y = 0.50x + 12

• x + y = 9.50

  x + y = 12.25

• y = 9x + 0.50

  y = 12x + 0.25

• y = 0.50x + 9

  y = 0.25x + 12

The volleyball team wants to order state tournament shirts. One company charges $12 per shirt and a $30 screen printing fee. Another company charges a $50 screen printing fee but only $8 per shirt. Which system of equations can be used to find the number of shirts when both companies charge the same amount?

• x + y = 12

  x + y = 8

• y = 12x + 30

  y = 8x + 50

• y = 12x + 30

  y = 50x + 8

• y = 12x + 8

  y = 30x + 50

Nobbies charges $1.50 per balloon and a $10 delivery fee. Party City charges $2.00 per balloon and $8 for delivery. Which system of equations will help find the number of balloons are needed for the cost from both stores to be the same?

• y = 10x + 1.50

  y = 8x + 2

• y = 1.50x + 2

  y = 10x + 8

• y = 1.50x + 10

  y = 2x + 8

• y = 1.50x + 8

  y = 2x + 10

One rental car company charges $25 per day and a $50 deposit. Another rental car company charges $40 per day. Which system of equations can you use to compare the total cost for renting a car from each complany?

• y = 75x

  y = 40x

• y = 50x + 25

  y = 40x

• y = 25x + 50

  y = 40x

• y = 50x + 25

  y = 40x

You often take the metro bus around the city. You have two payment options. For option 1, you buy a monthly pass and pay $1 per ride and a monthly pass costs $15. For option 2 you pay $2.50 per ride. Which system of equations will help find the number of rides it will take before the total costs of the two options are the same?

• y = x + 15

  y = 2.50

• y = 15x + 1

  y = 2.50x

• y = 2.50x + 15

  y = 1x + 15

• x + y = 15

  y = x - 2.50

Your car broke down while traveling home from a recent soccer tournament. Auto Towing charges $15 to pick you up and $0.50 per mile. Benny's Automotive Service charges $10 to pick you up but $0.75 per mile. Which system of equation can help find when Benny's Automotive Service cost less?

• y = 15 - 0.50x

  y = 10 - 0.75x

• y = 0.50x + 15

  y = 0.75x + 10

• y = 0.50x + 10

  y = 0.75x + 15

• 0.50x + 0.75x = 15

  x + y = 10

You need to repair a leaky faucet. One plumber charges $50 per hour and $100 to make a house call. Another plumber charges $50 to make a house call but $75 per hour. Which system of equations would help you find which plumber is most economical for a 3 hour repair job?

• y = 50x + 50

  y = 75x + 100

• x + y = 150

  x + y = 125

• y = 50x + 100

  y = 50x + 75

• y = 50x + 100

  y = 75x + 50

Tom and Luke started saving for college. Tom started with the $100 he got from his grandparents on his birthday and wanted to save $150 per month. Luke started with his summer job earnings of $500 and wanted to save $100 per month. Which system of equations will help find the number of months it will take for Tom's savings to surpass Luke's?

• y = 100 + 150x

  y = 500 + 100x

• y = 200x

  y = x + 600

• y = 100x + 150

  y = 500x + 100

• y = 100x + 100

  y = 150x + 500

Maria and Dianna were arguing about their summer jobs. Maria makes $8 per hour. Dianna makes only $3 per hour, but gets an additional $10 for the cost of uniforms. Which system of equations will help show how long they have to work before Dianna makes more?

• x + y = 8

  x + y + 10 = 3

• y = 8x

  y = 3x + 10

• y = 8x

  y = 10 - 3x

• y = 8x

  y = 13x

You are planning to take a summer trip with your basketball team. An amusement park charges a group rate of $10 per person with a $50 group fee. A water park charges a group fee of $20 and $13 per person. Which system of equations will help find which park is more economical for your eight member basketball team?

• y = 10x + 50

  y = 20 + 13x

• y = 10x + 50

  y = 20x + 13

• y = 50x + 10

  y = 13x + 20

• y = 13x + 50

  y = 10x + 20