Ms. McCullough Integrated Math 1

Solving Systems of Equations: Word Problems

“A high school choir is selling kits for plain cheese pizzas and pepperoni pizzas to

raise money for their spring trip. One student submitted an order for 23 pizza kits

with no indication of how many orders were for cheese and how many were for

pepperoni. The student also submitted a check for $187. If the cheese pizza kits

sell for $7 and the pepperoni pizza kits sell for $9, how many of each type of kit

were ordered?”

*The most difficult part of solving systems of equations in word problems is coming up with the actual

equations…I have outlined a few helpful hints that you can apply to almost any of these kind of

problems. *

In order to have a system of equations, you must have at least two different equations. Read the

following word problem above a few times before you decide how to attack it.

If you notice, the choir is selling 2 different pizza kits (cheese and pepperoni)…this gives you a hint that

you will be dealing with 2 different variables. Let’s name our first variable C (for cheese) and our second

variable P (for pepperoni).

The next thing to notice is that one student submitted an order for 23 pizza kits. In these types of

problems, there is usually an equation that focuses only on the total quantity, and then another that

factors in the total cost.

So, in this case, we know that the sum of our two types of pizza kits is 23. Therefore, we will use the

following equation for total quantity:

Now we can talk about the money! Notice that the total amount for the check was $187. They tell you

that the cheese pizza kits sell for $7 (that’s $7 each, or $7 per kit)…these key words should tell you that

you will be multiplying. They also tell you that the pepperoni pizza kits sell for $9 (that’s $9 each, or $9

per kit). The same rules apply for this one.

Since we know the total amount paid for the order (in dollars), we can use the following equation for

total cost:

The key question that the problem is asking is “how many of each type of kit were ordered?” Now we

have 2 variables and 2 equations, so you can choose which method you would like to use to solve for

each variable (graphically or algebraically…there are other ways to solve systems, which you will learn

about later). Good luck!