math word problem

Question

A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is 72$. he total cost to rent 3 chairs and 5 tables is 42$. What is the cost to rent each chair and each table?

cost to rent each chair_

Cost to rent each table_

Answer 1

Here's what we know:

9c + 7t = 72 (9 chairs and 7 tables cost $72)

3c + 5t = 42 (3 chairs and 5 tables cost $42)

Let's use the elimination method. Multiply the latter equation by -3 so we can subtract it from the former:

9c + 7t = 72

-9c - 15t = -126

-------------------------

-8t = -54

Divide both sides by -8:

t = 6.75

Now to find chairs:

3c + 5 * 6.75 = 42

3c + 33.75 = 42

Subtract 33.75:

3c = 8.25

Divide by 3:

c = 2.75

Check -- place the values into the first equation:

9 * 2.75 + 7 * 6.75 = 72

24.75 + 47.25 = 72

72 = 72