Modeling with Linear Systems Answers

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 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?

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?

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?

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?

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?

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?

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?

Hector and Francis spent a total of $47.50 at the mall. If Hector spent 50% more than Francis, how much did Francis spend at the mall?

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?