Modeling with Linear Systems Answers

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 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?

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?

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?

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?

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?

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?

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?

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?