Modeling with Linear Systems Answers

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?

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?

A school drama department sells 40 more student tickets than adult tickets. Charging $8 for adult tickets and $6 for student tickets, the drama department raises a total of $1,920 in ticket sales. Let x represent the number of adult tickets sold and y represent the number of student tickets sold. Which system of equations can be used to find how many of each ticket is sold?

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?

Abner wants to create a shopping budget where he spends less than $80 per month on school clothes and gym clothes combined. He also wants to spend at least three times as much on school clothes as on gym clothes. Let g represent the amount Abner spends on gym clothes per month, and let s represent the amount he spends on school clothes per month. Abner’s budget is represented by the graph below. Which statement is true?

Miguel and Beth like to play video games together. Miguel has m video games, and Beth has b video games. Miguel has 4 more video games than Beth, and together they have a total of 24 video games. Which system of equations can be used to find how many video games belong to each friend?

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?

At a cafe, the Bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. The Cortez family pays $14 for two salads and two sandwiches. The Donovan family pays $14 for a salad and three fruit bowls. What is the price of a fruit bowl at the cafe?

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?

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?