A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $52. The total cost to rent 9 chairs and 7 tables is $86. What is the cost to rent each chair and each table?

The cost for 1 chair is $2.75 and the cost for 1 table is $8.75

Step-by-step explanation:

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

1. Multiply the entire first equation by -3.

-3(3c+5t=52)

2. Simplify the equation from above:

-9c-15t=-156

3. Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

4. You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

5. Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

6. Simplify the equation above:

3c+43.75=52

7. Subtract 43.75 from both sides of the equation:

3c=8.25

8. Divide both sides by 3 to get your c value:

c=2.75