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:
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Renting 2 chairs and 6 tables costs $40: \[ 2C + 6T = 40 \]
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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:
- \( C + 3T = 20 \) (Equation 1)
- \( 5C + 3T = 25 \) (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
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