Calculating Fractions and Total Pies Sold at a School Fair: A Comprehensive Guide

School fairs are community events that often include a variety of activities and food stalls. One such activity involves selling pies with different fillings. In this guide, we will explore how to calculate the total number of pies sold and the fraction of pies that were filled with specific ingredients based on the information provided.

In one instance, at a school fair, 3/10 of the pies sold had cheese filling, 1/4 had beef filling, and the remaining 90 pies had potato filling. Let's break down the steps to find the fraction of pies with potato filling and the total number of pies sold.

Step-by-Step Calculation

To start, let's denote the total number of pies sold as X. We are given that:

3/10 of the pies had cheese filling 1/4 of the pies had beef filling The remaining 90 pies had potato filling

First, we calculate the fraction of pies that had either cheese or beef filling:

3/10 1/4 3/10 2.5/10 5.5/10 11/20

This means that 11/20 of the pies had either cheese or beef filling. Therefore, the fraction of pies with potato filling is:

1 - 11/20 9/20

Given that 90 pies represent the 9/20 that had potato filling, we can set up the following equation:

9x/20 90

Solving for X, we get:

x 90 * 20/9 200

This tells us that a total of 200 pies were sold at the fair.

Visualizing the Distribution of Pies

Now, let's break down the number of pies for each filling:

60 pies (3/10 of 200) had cheese filling 50 pies (1/4 of 200) had beef filling 90 pies (9/20 of 200) had potato filling

The total adds up to 200, confirming our calculation.

Conclusion

In conclusion, at this school fair, 9/20 of the pies had potato filling, and a total of 200 pies were sold. Understanding these calculations can help in planning and executing similar events more effectively.

If you need further assistance with similar problems or want to understand more about fractions and their practical applications, feel free to ask!