algebra word problem

Question

A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $77. The total cost to rent 3 chairs and 5 tables is $49. What is the cost to rent each chair and each table?

Answer 1

For this type of problem, you will need to set up a system of equations. This is because you have two variables, the number of chairs and the number of tables. You can assign x and y for your variables, but it might be more helpful to use c for chairs and t for tables.

9 c + 7 t = $77

3 c + 5 t = $49

to solve the system you can use elimination or substitution. Either will work, but I elimination appears easier here.

Multiply the second equation all the way through by -3 so that you have 9c on top and -9c on bottom.

9c + 7t = 77

-9c -15t = -147 Now add the equations

--------------------------

0 -8t = -70

t= 70/8 solve for t

t = $8.75 each table costs $8.75

Substitue this t value into one of the original equations to solve for c.

9c + 7(8.75) =77

9c = 15.75

c= $1.75 each chair costs $1.75