Of the cakes at Kirk's Bakery, 1/5 have chocolate frosting. Of the cakes with chocolate frosting, 2/5 have raspberry filling. What fraction of the cakes at Kirk's Bakery have both chocolate frosting and raspberry filling?

To solve this problem, let's break it down step by step:

1. **Fraction of cakes with chocolate frosting**:  
   \( \frac{1}{5} \) of the cakes at Kirk's Bakery have chocolate frosting.

2. **Fraction of chocolate-frosted cakes with raspberry filling**:  
   Of the cakes that have chocolate frosting, \( \frac{2}{5} \) have raspberry filling.

3. **Fraction of all cakes with both chocolate frosting and raspberry filling**:  
   To find this, multiply the fraction of cakes with chocolate frosting by the fraction of those that also have raspberry filling.

\[
\text{Fraction of all cakes with both chocolate frosting and raspberry filling} = \frac{1}{5} \times \frac{2}{5} = \frac{2}{25}
\]

So, \( \frac{2}{25} \) of the cakes at Kirk's Bakery have both chocolate frosting and raspberry filling.

Would you like further details or have any questions about this solution? Here are some related questions to consider:

1. If there are 100 cakes at Kirk's Bakery, how many have both chocolate frosting and raspberry filling?
2. What fraction of the cakes have either chocolate frosting or raspberry filling?
3. If 30 cakes have raspberry filling, what fraction of the cakes have raspberry filling but not chocolate frosting?
4. How would the solution change if instead \( \frac{3}{5} \) of the cakes with chocolate frosting had raspberry filling?
5. If \( \frac{3}{10} \) of all cakes have raspberry filling, what is the fraction of cakes without raspberry filling?

**Tip:** When dealing with fractions in word problems, break the problem into smaller steps, and multiply fractions to find combined probabilities.

Learn how to find the fraction of cakes at Kirk's Bakery with both chocolate frosting and raspberry filling. Step-by-step solution using fractions and probability concepts. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation