Modeling with Linear Systems Answers

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?

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?

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?

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 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?

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 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?

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?

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?