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Inequalities that Describe Patterns

Substitute values for variables to check inequality solutions

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Cheez Its
Teacher Contributed

Real World Applications – Algebra I

Topic

How are algebraic relationships represented in the nutrition facts of snacks?

Student Exploration

Below is a copy of the nutrition facts for a box of Cheez Its (Four Cheese), one of the most popular snack foods.

There are a lot of different ways that we can represent the information in this picture.

Let’s say that I’m addicted to Cheez Its and I can never really have just one serving size, which is 36 crackers. We can represent this relationship in a table.

# of serving size 0 1 2 3 4
# of crackers total 0 36 72 108 144

According to this table, 144 crackers eaten is equivalent to 4 servings! That’s a lot!

If we were to calculate the number of crackers in 10 servings, we can write this as an expression and figure it out. If x\begin{align*}x\end{align*} represents the number of serving sizes, the expression is 36x\begin{align*}36x\end{align*}. So, in 10 servings, I could eat 360 crackers. (I might also have a stomach ache too.)

We can also represent this relationship as an equation. If y represents the number of crackers, our equation would be y=36x\begin{align*}y = 36x\end{align*}. If I wanted to eat 200 crackers we can figure out how many serving sizes that would equate to. 200=36x\begin{align*}200 = 36x\end{align*}. We would divide both sides by 36, and find that x=5.6\begin{align*}x = 5.6\end{align*}, or a little over 5 and a half serving sizes.

When you get older, you will start to see that a lot of adults care about their calorie intake. According to the nutrition facts, one serving size has about 140 calories. People usually like to base what they eat on a 2000 calorie diet. Taking this fact into account, what is the maximum number of cheez its that I can eat in a day? Let’s create another equation to represent this relationship.

Let x\begin{align*}x\end{align*} represent the number of cheez its I eat, and let y\begin{align*}y\end{align*} represent the number of calories. Our equation is xy=36140\begin{align*}\frac{x}{y} = \frac{36}{140}\end{align*}. This special equation is also called a proportion. If we use multiplication to eliminate the denominators, our new equation is (140x)36=y\begin{align*}\frac{(140x)}{36} = y\end{align*}. Since we can’t exceed our 2000 calorie diet, our inequality is (140x)362000\begin{align*}\frac{(140x)}{36} \le 2000\end{align*}. What value of x\begin{align*}x\end{align*} would make this statement true?

We can use just two steps to figure this out! First, multiply both sides by 36 to eliminate the denominator. We now have 140x72000\begin{align*}140x \le 72000\end{align*}. Next, we divide both sides by 140. So, x514.3\begin{align*}x \le 514.3\end{align*}. This means that I can’t eat more than 514 crackers in one day, assuming that’ll be the ONLY food I eat all day.

Now we have the maximum amount of crackers I can have in one day, how many servings is this?

51436=14\begin{align*}\frac{514}{36} = 14\end{align*} servings.

Note: It is not suggested that a person eat 514 Cheez Its!

Extension Investigation

Try looking at the nutrition facts label on your favorite food, and figure out what the maximum amount you can eat of that particular food, based on a 2000 calorie diet.

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