Question
Jennie bought a bag of jelly beans from Sweet Tooth Confectionery. There are 14 cherry jelly beans in the bag. If \( \frac{2}{5} \) of the bag is cherry, how many total jelly beans, \( j \), are in the bag?
Ask by Burns Rodriguez. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 35 jelly beans in the bag.
Solution
To determine the total number of jelly beans in the bag, let's break down the problem step by step.
**Given:**
- Number of cherry jelly beans = 14
- Cherry jelly beans constitute \( \frac{2}{5} \) of the total jelly beans.
**Let \( j \) represent the total number of jelly beans in the bag.**
**Step 1: Set Up the Equation**
Since \( \frac{2}{5} \) of the total jelly beans are cherry, we can write the equation as:
\[
\frac{2}{5} \times j = 14
\]
**Step 2: Solve for \( j \)**
To find \( j \), multiply both sides of the equation by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):
\[
j = 14 \times \frac{5}{2}
\]
\[
j = 14 \times 2.5
\]
\[
j = 35
\]
**Answer:**
There are **35** jelly beans in the bag.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the total number of jelly beans in the bag, you can set up the equation based on the information given. Since \(\frac{2}{5}\) of the bag is cherry jelly beans and there are 14 cherry jelly beans, you can express it as: \[ \frac{2}{5}j = 14 \] To solve for \(j\), multiply both sides by \(\frac{5}{2}\): \[ j = 14 \times \frac{5}{2} = 14 \times 2.5 = 35 \] So, there are a total of 35 jelly beans in the bag. Now you can enjoy munching on those jelly beans, knowing there’s a sweet total in the bag!
