Tricia manages a health bar and wants to add a new fruit and protein smoothie to the menu. To decide on the new flavor she plans to offer. Tricia sold trial-sized banana smoothies and kiwi smoothies. She charged $2 for a banana smoothies and $2.50 for a kiwi smoothies and she told 40 in all, totalling $87. How much more maney did Tricia make on the banana smoothies than the kiwi smoothies?

Options

A. 12
B. 17
C. 26
D. 52

Explanation

To solve the problem step by step, we will set up equations based on the information given in the question.

### Step 1: Define the Variables
Let:
- \( B \) = number of banana smoothies sold
- \( K \) = number of kiwi smoothies sold

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of smoothies sold (banana + kiwi) is 40:
\[ B + K = 40 \]
2. The total revenue from selling the smoothies is $87. The revenue from banana smoothies is $2 per smoothie and from kiwi smoothies is $2.50 per smoothie:
\[ 2B + 2.5K = 87 \]

### Step 3: Solve the First Equation for One Variable
From the first equation, we can express \( B \) in terms of \( K \):
\[ B = 40 - K \]

### Step 4: Substitute into the Second Equation
Now, substitute \( B \) in the second equation:
\[ 2(40 - K) + 2.5K = 87 \]
Expanding this gives:
\[ 80 - 2K + 2.5K = 87 \]
Combining like terms:
\[ 80 + 0.5K = 87 \]

### Step 5: Isolate \( K \)
Subtract 80 from both sides:
\[ 0.5K = 7 \]
Now, divide by 0.5:
\[ K = 14 \]

### Step 6: Find \( B \)
Now that we have \( K \), substitute back to find \( B \):
\[ B = 40 - K = 40 - 14 = 26 \]

### Step 7: Calculate the Revenue from Each Type of Smoothie
Now, calculate the revenue from banana smoothies and kiwi smoothies:
- Revenue from banana smoothies:
\[ \text{Revenue from bananas} = 2B = 2 \times 26 = 52 \]
- Revenue from kiwi smoothies:
\[ \text{Revenue from kiwis} = 2.5K = 2.5 \times 14 = 35 \]

### Step 8: Find the Difference in Revenue
Now, find how much more money Tricia made on banana smoothies than on kiwi smoothies:
\[ \text{Difference} = \text{Revenue from bananas} - \text{Revenue from kiwis} = 52 - 35 = 17 \]

### Final Answer
Tricia made $17 more on banana smoothies than on kiwi smoothies.

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