Problem Solving with Systems Answers

Company A sells hats for $11 per hat plus a fixed $7 shipping and handling fee. Company B sells hats for $8 per hat plus a fixed $16 shipping and handling fee. The marketing director of company A wants to set up a system of equations to find the number of hats for which the total cost of an order for the two companies is the same. He uses the variables x and y. He lets y represent the total cost of an order. What will x represent?

The monthly texting plan of All Star Cell is $11 per month and $0.25 per text. The monthly texting plan of Top Line Cell is $14 per month and $0.15 per text. A student wants to set up a system of equations to find the number of texts for which the total monthly cost of the two companies is the same. He uses the variables x and y. He lets y represent the total monthly cost. What will x represent?

Trina downloaded 3 music albums and 5 audio books one week at a cost of $49.60. The next week she downloaded 1 music album and 2 audio books at a cost of $20.50. Her mother wants to write a system of equations to determine the price of one music album and one audio book. She uses the variables x and y. She lets x represent the cost of one music album. What will y represent?

Tickets for a celebrity golf tournament were sold before the tournament and on the day of the tournament. After reviewing ticket sales, the tournament director found that 150 fewer tickets were purchased on the day of the tournament than before the tournament. A total of 898 tickets were sold. How many tickets were sold on the day of the tournament?

Which is the best first step when solving the following system of equations?

Mrs. Rodrigues was selling two kinds of raffle tickets for $1.50 and $3.50. The number of $1.50 tickets sold was 5 more than three times the number of $3.50 tickets sold. She earned a total of $1,607.50. How many $1.50 tickets were sold?

Mario sold concessions during the hockey tournament at the high school. He sold bottled water for $2.50 each and hamburgers for $5.50 each. By the end of the tournament, Mario’s sold 350 items for a total of $1,325. Which statements about the concession sales are true? Check all that apply.

Aeva is selling friendship pins as a service project. Each pin with green beads sells for $3. Each pin with red beads sells for $2. She raised $312. The number of pins with green beads is 11 fewer than the number of pins with red beads. How many red pins did Aeva sell?

Shenika is selling magazine subscriptions for the animal shelter. A yearly subscription to a story magazine is $12.50. A yearly subscription to a puzzle magazine is $14. She raised a total of $1,225 for the animal shelter. The number of subscriptions to the story magazine, s, is 20 more than twice the number of subscriptions to the puzzle magazine, p. Which system of equations finds the number of each magazine sold?

The local high school hosted a hockey tournament. Tickets were sold before the tournament and at the door. When reviewing the ticket sales, the director of the tournament realized that there were 80 more tickets purchased before the tournament than at the door. A total of 820 tickets were sold. Which statements about ticket sales are true? Check all that apply.