Modeling with Linear Systems Answers

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?

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?

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 digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

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?

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?

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?

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?

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?

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?