Algebra IName:______Linear System Word Problems
1) Tyler needs to rent a truck. Suppose Company A charges a $15 fee plus $25 per day. Company B charges a $40 fee plus $20 per day.
a. Write a system of equations that Tyler could use to figure out how much it would cost him to use either company.
a. Tyler says it will cost him the same amount to use either company, how many days does he plan on renting a truck?
b.Graph your equations on the axis provided below.
c. Based on the graph, which company should he rent from if he needs the truck for 7 days?
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. Use the space below to answer/solve the following questions.
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 a system of 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) Alexia and Isabella both work at the mall. Alexia makes $32 a week plus $2 per hour she works. Isabella makes $16 a week plus $6 per hour she works. Use the space below to answer/solve the following questions.
a. Write a system of equations that models how much money Alexia and Isabella make per week.
b. How many hours would Alexia and Isabella 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) Anna and Christina want to join a gym. Anna’s gym requires an $80 startup fee along with paying $20 a month. Christina’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 Anna and Christina to pay the same amount?
c.Graph your equations on the axis provided.
d. Use your graph above to answer the following question: If Anna and Christina want to join the gym for 5 months, whose gym is cheaper?