Please Help Me With This Word Problem

Question

A party rental company has chairs and tables for rent. The total cost to rent 2

 chairs and 6

 tables is $42

. The total cost to rent 5

 chairs and 3

 tables is $30

. What is the cost to rent each chair and each table?

Answer 1

Hi Domenic,

Let's use the variable, c, represent the cost of 1 chair and the variable, t, represent the cost of 1 table.

We can write the following equations to represent the situation described in your problem:

2c + 6t = 42

5c + 3t = 30

Now we can solve these two equations with two unknowns to find the cost of each chair or table.

Multiply the second equation by -2 to find the cost of 1 chair:

5c + 3t = 30 becomes -10c - 6t = -60

Now combine this "new" equation with the original first one:

2c + 6t = 42

-10c - 6t= -60

-8c = -18

c = 18/8 or $2.25

The cost to rent 1 chair was $2.25

Now substitute this value for c into either original equation to find the cost to rent 1 table:

2c + 6t = 42

2 • 2.25 + 6t = 42

4.50 + 6t = 42

4.50 + 6t - 4.50 = 42 - 4.50

6t = 37.50

t= %6.25

The cost to rent 1 table was $6.25