Math Homework for school

Question

A party rental company has chairs and tables for rent. The total cost to rent 2

 chairs and 3

 tables is $31

. The total cost to rent 6

 chairs and 5

 tables is $59

. What is the cost to rent each chair and each table? 

Answer 1

Form 2 simultaneous equations as follows (note C=chair and T=table):

(1) 2C + 3T = $31

(2) 6C + 5T = $59.

Multiply all terms of (1) by -3 to get

(1a) -6C -9T = -93

Add (1a) to (2) to get

0C -4T = -34 ==> -4T = -34

Divide both sides by -4 to find T = $8.50, the cost to rent each table.

Plug this value in place of T in (1) or (2) to find C:

(1) 2C + 3(8.50) = 31.00 ==> 2C + 25.50 = 31.00 ==> 2C = $5.50.

Divide by 2 to get C = $2.75, the cost of renting each chair.

(2) 6C + 5(8.50) = 59.00 ==> 6C + 42.50 = 59.00 ==> 6C = $16.50.

Divide by 6 to get C = $2.75, the cost of renting each chair.