Question

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $40. The total cost to rent 5 chairs and 3 tables is $25.
What Is the cost to rent each chair and each table?

Answer 1

Let's denote the cost to rent one chair as \( C \) and the cost to rent one table as \( T \).

From the information given in the problem, we can set up the following system of equations based on the rentals:

1. Renting 2 chairs and 6 tables costs $40:
\[
2C + 6T = 40
\]

2. Renting 5 chairs and 3 tables costs $25:
\[
5C + 3T = 25
\]

Now, we can solve this system of equations.

**Step 1:** Let's simplify the first equation. We can divide the entire equation by 2:
\[
C + 3T = 20 \quad \text{(Equation 1)}
\]

**Step 2:** Now we have:
1. \( C + 3T = 20 \) (Equation 1)
2. \( 5C + 3T = 25 \) (Equation 2)

**Step 3:** We can eliminate \( T \) by subtracting Equation 1 from Equation 2:
\[
(5C + 3T) - (C + 3T) = 25 - 20
\]
This simplifies to:
\[
4C = 5
\]
Now, we can solve for \( C \):
\[
C = \frac{5}{4} = 1.25
\]

**Step 4:** Now that we have the value of \( C \), we can substitute it back into Equation 1 to find \( T \):
\[
1.25 + 3T = 20
\]
Subtract \( 1.25 \) from both sides:
\[
3T = 20 - 1.25
\]
\[
3T = 18.75
\]
Now, divide by 3:
\[
T = \frac{18.75}{3} = 6.25
\]

Thus, the cost to rent each chair and each table is:
- Cost of each chair \( C = 1.25 \) dollars
- Cost of each table \( T = 6.25 \) dollars

In conclusion:
- Cost of each chair = **$1.25**
- Cost of each table = **$6.25**