Name: ___________________________________________________ Hour _______
Linear Systems
For each problem you will need to:
a. Define the variables (Let x = …, Let y = …)
b. Write 2 equations to represent the given information
c. Use substitution or elimination: SHOW WORK
d. State your solution in sentence form
1. Find the value of two numbers whose sum is 12 and whose difference is 4.
2. Corey and Gabi are selling pies for a school fundraiser. Customers can buy apple pies and lemon
meringue pies. Corey sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabi sold 6
apple pies and 5 lemon meringue pies for a total of $94. What is the cost each of one apple pie and
one lemon meringue pie.
3. The local amusement park is a popular field trip destination. This year the senior class at Meridian
High School rented and filled 16 vans and 8 buses with 752 students. Freeland High School rented
and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of
students. How many students can a van carry? How many students can a bus carry?
4. The perimeter of a rectangular park is 95 feet. The length is 2 feet more than twice the width.
Find the dimension of the garden.
5. A plane traveled 580 miles to Washington D.C. and back. The trip there was with the wind. It took
5 hours. The trip back was into the wind and took 10 hours Find the speed of the plane in still air and
the speed of the wind. (Distance = rate x time or D = rt)
6. You worked 14 hours last week and earned a total of $96 before taxes. Your job as a lifeguard
pays $8 per hour and your job as a cashier pays $6 per hour. How many hours did you work at each
job?
7. The price of refrigerator A is $600, and the price of refrigerator B is $1200. The cost of electricity
needed to operate the refrigerators is $50 per year for A and $40 per year for B. After how many
years are the total costs of owning the refrigerators equal? Would it be cost effective to purchase
refrigerator B? Explain.