Marisol is selling snacks at her school's soccer games to raise money for a service project. She boys nuts in cases that contain 24 gags and granolda bars in cases that contain 20 packages. She sells the nuts for `$1.25` a bag and the granola bars for `$1.75` a package. If she raised `$160` and sold 112 items, how many cases of granolsa bars did Marisol buy ?

Options

A. 2
B. 3
C. 40
D. 72

Explanation

To solve the problem, we will set up a system of equations based on the information provided.

### Step 1: Define Variables
Let:
- \( x \) = total number of bags of nuts sold
- \( y \) = total number of packages of granola bars sold

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of items sold (nuts and granola bars) is 112:
\[ x + y = 112 \quad \text{(Equation 1)} \]

2. The total amount raised from selling these items is $160. The selling prices are $1.25 per bag of nuts and $1.75 per package of granola bars:
\[ 1.25x + 1.75y = 160 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
To eliminate the decimals, we can multiply the entire Equation 2 by 4:
\[ 5x + 7y = 640 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 1 into Equation 3
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 112 - y \]

Now substitute \( x \) into Equation 3:
\[ 5(112 - y) + 7y = 640 \]

### Step 5: Solve for \( y \)
Expanding the equation:
\[ 560 - 5y + 7y = 640 \]
Combine like terms:
\[ 560 + 2y = 640 \]
Subtract 560 from both sides:
\[ 2y = 80 \]
Divide by 2:
\[ y = 40 \]

### Step 6: Find \( x \)
Now substitute \( y \) back into Equation 1 to find \( x \):
\[ x + 40 = 112 \]
Subtract 40 from both sides:
\[ x = 72 \]

### Step 7: Calculate the Number of Cases of Granola Bars
Since each case of granola bars contains 20 packages, the number of cases of granola bars Marisol bought is:
\[ \text{Number of cases} = \frac{y}{20} = \frac{40}{20} = 2 \]

### Final Answer
Marisol bought **2 cases of granola bars**.

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