System of Equations Word Problems

Question

A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38. The total cost to rent 2 chairs and 5 tables is $35. What is the cost to rent each chair and each table?

Answer 1

If we convert the word problem into equations, then we get the following.

(C and T stand for the price of chairs and tables respectively)

8C+3T=38

2C+5T=35

We can multiply the second equation by 4 so both equations have an 8C in them.

8C+3T=38

8C+20T=140

We can subtract the first equation from the second to cancel out the 8C in both equations.

(8C+20T)-(8C+3T)=140-38

17T=102

Divide by 17 to isolate T.

T=6

Once we have one value, we can substitute it into any equation with T and C. I will be using 2C+5T=35.

2C+5(6)=35

2C+30=35

2C=5

C=2.5

From this, we know that one chair is worth $2.50 and one table is worth $6.

Answer 2

To do these types of problems, first assign a variable name to what you need to find out. Say, C = cost of each chair, and T = cost of each table.

Next, figure out the equations based on the words in the problem:

8C + 3T = 38

2C + 5T = 35

There are two ways to solve this "system of equations". Substitution or Elimination. Unless you teacher specifies which method, you can use either method, which ever you like.

Substitution: First, you use algebra to get one of the variables by itself on one side of the equation:

2C + 5T = 35 => 2C = 35 - 5T => C = 35/2 - 5/2 T

Then substitute that in the other equation and then get that variable on one side of the equation:

8(35/2 - 5/2 T) + 3T = 38

140 - 20T + 3T = 38

-17T = -102

T = -102/-17 = 6

Then plug 6 back into either equation 2C + 5x6 = 35 => C = 2.5

Elimination. For this method, you multiple one of the equations by some number so the coefficients match for one of the variables. (You have to multiply everything in the equation!)

8C + 3T = 38

(2C + 5T = 35) x 4 = 8C + 20T = 140

Then subtract the corresponding terms of the equations. 8C - 8C = 0, 3T - 20T = -17, 38 - 140 = -102, so you end up with

-17T = -102, which is T = 6. And plug 6 back into either equation to get C = 2.5.

So, each table costs $6 and each chair costs $2.50.

It's always good to check to make sure you got the right answer by plugging the numbers into both equations to make it's true.

Answer 3

System of equations problem:

T = cost to rent table; C = cost to rent chair

(1) 8C + 3T = 38

(2) 2C + 5T = 35

Suggest you use the elimination method to remove the "C" terms. Best is to mult eqn (2) by -4 and add the two equations, then solve for T. Once you have T, can use that in either (original) eqn to find "C".

Hint: C involves dollars and cents.