Solving a word problem using linear equation

Question

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $39. The total cost to rent 9 chairs and 7 tables is $63. 

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

Cost to rent each chair:

Cost to rent each table:

Answer 1

Step 1: Define the variables

Let x= Cost of Chair

Let y= Cost of Table

Step 2: Setup a system of equations

3x+5y=39

9x+7y=63

Step 3: Solve the system using elimination

a) Mult (-3) times Equation 1

(-3)(3x+5y=39)

-9x-15y=-117

b) Add Equation 1 to Equation 2

-9x-15y=117

9x + 7y = 63

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

-8y=-54

y= $6.75

c) Substitute your solution for y into Equation 1

3x + 5(6.75) = 39

3x + 33.75 = 39

3x = 5.25

x= $1.75

Step 4: Check your solution.

3(1.75) + 5(6.75) = 39

9(1.75) + 7(6.75) = 63

Step 5: State your answer.

$6.75 is the cost of a table and $1.75 is the cost of a chair

Answer 2

1) 3c + 5t = 39

2) 9c + 7t = 63

Multiply equation 1) by 3

4) 9c + 15t = 117

2) 9c + 7t = 63

Subtract 2) from 4)

5) 8t = 54

6) t = 27 / 4

Review the data for accuracy.