Question

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $21. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?

Answer 1

Let's say the cost to rent each chair is "x" and the cost to rent each table is "y". Then we can set up two equations based on the given information:

3x + 2y = 21 (for the first rental)

8x + 4y = 45 (for the second rental)

We can simplify the second equation by dividing both sides by 4:

2x + y = 11.25

Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:

3x + 2y = 21

2x + y = 11.25

From the second equation, we can solve for y in terms of x:

y = 11.25 - 2x

Then we can substitute this expression for y in the first equation:

3x + 2(11.25 - 2x) = 21

Simplifying and solving for x, we get:

3x + 22.5 - 4x = 21

-x + 22.5 = 21

-x = -1.5

x = 1.5

So the cost to rent each chair is $1.50. We can substitute this value back into either of the original equations to solve for y:

3(1.5) + 2y = 21

4.5 + 2y = 21

2y = 16.5

y = 8.25

So the cost to rent each table is $8.25. Therefore, the answer is $1.50 for each chair and $8.25 for each table.