A party rental company has chairs and tables for rent.

Question

A party rental company has chairs and tables for rent. The total cost to rent
2
chairs and
5
tables is
$53
. The total cost to rent
8
chairs and
3
tables is
$42
. What is the cost to rent each chair and each table?

Answer 1

The information given can be written in two equations using c as the variable for the cost of renting chairs, and t as the variable for the cost of renting tables:

 

2c + 5t = 53

 

8c + 3T = 42

 

The subtraction method for solving a two equation system is very convenient in this case. To do that, first multiply the entire first equation by 4 turning it into:

 

8c + 20t = 212

 

Then subtract the second equation from this:

 

   8c + 20t = 212

 

 -(8c + 3t  =  42

______________

 

   0c + 17t = 170

 

Solving for t, t = 10. Now plug that in to get c.

 

2c + 5t = 53, substitute 10 for t:

 

2c + 50 = 53. subtract 50 from each side:

 

2c = 3. Solve for c.

 

c = 1.5

 

It costs 10 dollars to rent a table, and 1.5 dollars to rent a chair.