Question

A party rental company has chairs and tables for rent. The total cost to rent 7 chairs and 9 tables is $91. The total cost to rent 5 chairs and 3 tables is $35. What’s the cost to rent each chair and each table?

Answer 1

Let \( c \) be the cost to rent one chair and \( t \) be the cost to rent one table. We can set up the following system of equations based on the information given:

1. From the first scenario:
\( 7c + 9t = 91 \) \quad (Equation 1)

2. From the second scenario:
\( 5c + 3t = 35 \) \quad (Equation 2)

Now we can solve this system of equations.

First, let's solve Equation 2 for one of the variables. We'll solve for \( c \):

\[
5c + 3t = 35
\]

Subtract \( 3t \) from both sides:

\[
5c = 35 - 3t
\]

Now divide by 5:

\[
c = \frac{35 - 3t}{5} \quad (Equation 3)
\]

Next, substitute Equation 3 into Equation 1:

\[
7\left(\frac{35 - 3t}{5}\right) + 9t = 91
\]

Multiply everything by 5 to eliminate the fraction:

\[
7(35 - 3t) + 45t = 455
\]

Distribute the 7:

\[
245 - 21t + 45t = 455
\]

Combine like terms:

\[
245 + 24t = 455
\]

Now, subtract 245 from both sides:

\[
24t = 210
\]

Now divide by 24:

\[
t = \frac{210}{24} = \frac{35}{4} = 8.75
\]

Now that we have the cost of a table, substitute \( t \) back into Equation 3 to find \( c \):

\[
c = \frac{35 - 3(8.75)}{5}
\]

Calculate \( 3(8.75) \):

\[
3(8.75) = 26.25
\]

Now substitute it back into the equation for \( c \):

\[
c = \frac{35 - 26.25}{5} = \frac{8.75}{5} = 1.75
\]

So, the costs are:

\[
\text{Cost of each chair } c = 1.75
\]
\[
\text{Cost of each table } t = 8.75
\]

Thus, the cost to rent each chair is \( \boxed{1.75} \) and the cost to rent each table is \( \boxed{8.75} \).