Modeling with Linear Systems Answers

A movie theater has 400 seats. Tickets at the theater cost $8 for students, $10 for adults, and $7 for senior citizens. On a night when all the seats were sold, the theater made $3,535 from ticket sales. If the number of adult tickets sold was 10 less than the number of student and senior tickets combined, how many senior tickets were sold?

Pam laid three times as many tiles on Saturday as she laid on Sunday. If Pam laid 80 tiles over the weekend altogether, how many tiles did she lay on Saturday?

Lisa leaves a gas station and drives at an average rate of 50 mi/hr. Keisha leaves the gas station one hour later and drives along the same route at an average rate of 60 mi/hr. Let d represent the distance driven in miles and t represent the time since Lisa left the gas station. Which system of equations can be used to find how long after Lisa left the gas stations that she is passed by Keisha?

A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width in inches of the picture frame, and let l represent the length in inches. Which system of equations can be used to find the dimensions of the picture frame?

The concession stand at the local high school sells pretzels and lemonade. The total cost of two pretzels and a lemonade is $5.75. The total cost of two lemonades is $0.25 more than the cost of a pretzel. What is the cost of a pretzel?

Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

The given system of equations models the coins in a jar containing n nickels, d dimes, and q quarters. Which statement is modeled by one of the equations in the system?

Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes at three-quarters the rate she biked to the market. If the trip home takes 12 minutes longer than the trip to the market, how many minutes does it take Carmen to bike home?

Duncan has the space to plant, at most, 24 flower bulbs in his garden. Daffodil bulbs cost $3 each, and tulip bulbs cost $2 each. Duncan does not wish to spend more than $60 on his garden. Which set of bulbs satisfies Duncan’s constraints?

The Carson family paid $192 for two adult and three youth tickets to an amusement park. At the same park, the Davis family paid $148 for one adult and four youth tickets. Let x represent the cost of an adult ticket, and let y represent the cost of a youth ticket. Which system of equations can be used to find the cost of each ticket?