Advanced Algebra I Name:______Linear System Word Problems
1) Eric wants to drive to Disney World and needs to rent a car. Suppose Company A charges a $15 fee plus $30 per day. Company B charges a $60 fee plus $20 per day.
a. Eric says it will cost him the same amount to use either company, how many days does he plan on renting a car?
b.Graph your equations on the axis provided.
c. Based on the graph, which company should he rent from if he needs the car for 7 days? Validate your decision algebraically.
2) Matt is going to a Knicks game and is trying to decide where to park. The garage on 36th street charges a fee of $6 plus $10 per hour, while the garage on 35th street charges a $2 fee plus $12 an hour.
a. What question would you ask Matt to help him make his decision? (Assume that he only cares about how much he would pay).
b. Write an equation or equations that models how much it would cost Matt to park in either garage.
c. For exactly how many hours would Matt have to park his car so that it doesn’t matter which garage he uses?
d. Confirm your solution to part c using the graph provided.
3) Lauren and Olivia both work at Old Navy. Lauren makes $32 a week plus $2 per hour she works. Olivia makes $16 a week plus $6 per hour she works.
a. Write an equation or equations that models how much money Lauren and Olivia make per week.
b. How many hours would Lauren and Olivia have to work in a week so that they make the same amount of money?
c. Confirm your solution to part b on the graph provided.
4) Gabrielle and Brendan want to join a gym. Garbielle’s gym requires an $80 startup fee along with paying $20 a month. Brendan’s gym has no startup fee, but she has to pay $60 each month.
a. Write a system of equations that models the situation above.
b. How many months will it take for Gabrielle and Brendan to pay the same amount?
c. Graph your equations on the axis provided.
d. Use your graph above to answer the following question: If Gabrielle and Brendan want to join the gym for 5 months, whose gym is cheaper?