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A bakery sells two types of cakes: Chocolate and Vanilla. The sales percentages for each type are 60% and 40%, respectively.

If the average price of a Chocolate cake is [tex]$25[/tex] and the average price of a Vanilla cake is [tex]$30[/tex], what is the overall average price of cakes sold by the bakery?

Answer :

Sure! Let's go through the steps to find the overall average price of all cakes sold by the bakery.

### Step 1: Understand the Given Information
- Sales percentages:
- Chocolate cakes: 60% (or 0.60 in decimal form)
- Vanilla cakes: 40% (or 0.40 in decimal form)
- Prices:
- Average price of a Chocolate cake: [tex]$25
- Average price of a Vanilla cake: $[/tex]30

### Step 2: Calculate the Contribution of Each Type of Cake to the Overall Average Price
To find the overall average price, we need to consider the weight (percentage) and the price of each type of cake.

1. Contribution of Chocolate cakes to the overall average price:
[tex]\[
0.60 \times 25 = 15
\][/tex]

2. Contribution of Vanilla cakes to the overall average price:
[tex]\[
0.40 \times 30 = 12
\][/tex]

### Step 3: Add the Contributions Together
Now, add the contributions from both Chocolate and Vanilla cakes to get the overall average price.

[tex]\[
15 + 12 = 27
\][/tex]

### Conclusion
The overall average price of cakes sold by the bakery is $27.00.

I hope this helps! If you have any more questions, feel free to ask.

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