Question

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?

Answer 1

The cost to rent each chair is $2.75 and the cost to rent each table is $8.75.

Step-by-step explanation:

To solve this problem, let's assign variables to the cost of renting a chair and a table. Let's say the cost of renting a chair is $x and the cost of renting a table is $y.

From the given information, we can set up two equations:

3x + 5y = 52 (Equation 1)

9x + 7y = 86 (Equation 2)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiply Equation 1 by 3 and Equation 2 by 1:

9x + 15y = 156 (Equation 3)

9x + 7y = 86 (Equation 2)

Now, subtract Equation 2 from Equation 3:

9x + 15y - 9x - 7y = 156 - 86

8y = 70

Divide both sides of the equation by 8:

y = 8.75

Substitute the value of y back into Equation 1:

3x + 5(8.75) = 52

3x + 43.75 = 52

Subtract 43.75 from both sides:

3x = 8.25

Divide both sides of the equation by 3:

x = 2.75

Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.75.

Answer 2

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