Introduction

Judy is a fun-loving girl who loves to share. One day, she decides to share 7/8 of her walnut candy bars with her friends. If she gives one candy bar to each of her 28 friends, how many candy bars will she need before starting to share?

Let's break down the problem step by step to find the answer.

Problem Solving: Applying Math to Real-Life Situations

The number of candy bars Judy needs to give to her friends can be calculated easily. We need to determine how many candy bars are needed so that 7/8 of them equals 28 candy bars.

Step-by-Step Solution

Understanding the Fraction: To find out the total number of candy bars before sharing, we need to reverse the given fraction. That is, if 7/8 of the candy bars amounts to 28, we can find the whole by dividing 28 by 7 and then multiplying by 8. Divide by the Numerator: First, we perform the operation: 28 / 7 4. Multiply by the Denominator: Then, we multiply the result by 8: 4 * 8 32. Conclusion: Judy will need 32 candy bars before starting to share them. This means that when she gives one candy bar to each of her 28 friends, she will distribute 7/8 of the total and will be left with 1/8, or 4 candy bars for herself.

Alternatively, we can use algebra to solve this problem. Let's denote the total number of candy bars Judy needs as x. The equation would be:

7/8x 28

Solving for x:

Isolate the Variable: Multiply both sides by 8/7 to solve for x: x 28 * (8/7) 32. Conclusion: Again, we find that Judy needs 32 candy bars before sharing.

Tackling the Peanut Allergy Issue

It's crucial to consider any dietary restrictions among Judy's friends. While the question does not mention anyone with a peanut allergy, it's always important to ensure that the candies being shared are safe for everyone to consume. If there are any friends with allergies, Judy should choose an alternative treat that suits everyone's dietary needs.

Mathematics Behind Sharing: A Cheat Sheet

When dealing with fractions and sharing in real-life situations, remember these key steps:

Identify the fraction representing the portion to be shared. Set up an equation if necessary, where the total amount multiplied by the fraction equals the shared amount. Solve the equation to find the total amount of items needed. Verify your answer by checking if the calculated number makes sense in the context of the problem.

By following these steps, you can easily solve similar sharing problems involving fractions and real-world scenarios.

Conclusion

From this problem, it's clear that Judy will need 32 walnut candy bars to share with her 28 friends, leaving herself with 4 candy bars. This example demonstrates the practical application of fraction arithmetic and the importance of considering additional factors, such as dietary restrictions, in sharing situations. So next time you face a similar situation, you can apply the methods discussed here to find the solution.