A party rental company has chairs and tables for rent.

Question

The total cost to rent
2
chairs and
3
tables is
$35
. The total cost to rent
6
chairs and
5
tables is
$63
. What is the cost to rent each chair and each table?

Answer 1

There are several ways to get at the answer. I'm going to show you the combination method for systems of equations.

 

Let's use x for chairs and y for tables.

So we know 2x + 3y = 35 and 6x +5y = 63
We line them up in columns.  (To make it easier later, I'll switch the order.)
6x + 5y = 63

2x + 3y = 35

 

To eliminate the x variable, I'll multiply every element in the 2nd equation by -3.  

 6x + 5y =   63
-6x - 9y = -105

 

Now we combine (add) the equations, which eliminates x altogether.
-4y = -42 ... 4y = 42 ... y = 10.50

 

From there we can substitute in either equation to solve for x.

2x + (3*10.50) = 35 ... 2x + 31.50 = 35 ... x = 1.75

 

A very important thing to remember using this method is to do the same thing to each element in the equation that you change!