Problem Solving with Systems Quiz

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.

--The variable x could represent the number of tickets sold before the tournament. --The variable y could represent the number of tickets sold at the door. --The system of equations that could represent this situation is x+y=820 x-y=80

At a farmer's market, Khalid bought 4 pounds of tomatoes and 7 pounds of broccoli for $28. Genevieve bought 5 pounds of tomatoes and 2 pounds of broccoli for $28.50. Let t represent the cost of one pound of tomatoes. Let b represent the cost of one pound of broccoli. Which system of equations will solve for t and b?

4t+7b=28.00 5t+2b=28.50

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?

Incorrect: 748 tickets

Tickets for a school jazz concert were sold before the concert and at the door. After reviewing ticket sales, the band director found that 80 fewer tickets were purchased at the door than before the concert. A total of 520 tickets were sold. Let d represent the number of tickets sold at the door and b represent the number of tickets sold before the concert. Latifa wrote the following system of linear equations to find the number of each type of ticket sold: d+b=520 d-80=b What is Latifa's error?

Incorrect: Latifa should have written the first equation as b+80=520

A college is selling tickets for a winter fund-raiser. One day, Krissa sold 14 adult tickets and 8 student tickets for a total of $376. The next day, she sold 7 adult tickets and 11 student tickets for a total of $272. Krissa wanted to find the price of one adult ticket, a, and the price of one student ticket, s. She wrote and solved the following system of equations. 14a+8s=376 7a+11s=272 She found that the price of one student ticket is $20 and the price of one adult ticket is $12. Which statement explains Krissa's error?

Incorrect: She did not write the correct system of equations.

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?

x = number of texts

Best Company sells personalized mugs for $18 each plus a fixed fee of $26 for shipping and handling for the entire order. The Cup Expert Company sells personalized mugs for $22 each plus a fixed fee for $14 for shipping and handling for the entire order. How many personalized mugs would a customer have to purchase for the total cost of each company to be the same?

3 mugs

One Friday night, a group of friends bought 5 containers of popcorn and 4 granola bars at the movie theatre for $42.50. The next week, the same group of friends bought 3 containers of popcorn and 6 granola bars for $34.50. Let p represent the cost of one container of popcorn. Let g represent the cost of one granola bar. Which system of equations will solve for p and g?

5p+4g=42.50 3p+6g=34.50

The town glee club sold tickets for the summer concert. The club charged $8 for a child ticket and $18 for an adult ticket. A total of $8,400 in ticket sales was raised. The number of adult tickets, a, is 50 more than twice the number of child tickets, c. Which system of equations will solve for the number of each type of ticket?

8c+18a=8,400 a=2c+50

Which is the best first step when solving the following system of equations? x+y=3 4x-y=7

Incorrect: Subtract the second equation from the first equation.