Problem:
A local bakery sells two types of bread: white bread and whole wheat bread. The bakery conducted a survey to determine the number of loaves of each type of bread sold in a week. The survey results showed that the bakery sold a total of 120 loaves of bread, and the number of white bread loaves sold was 20 more than the number of whole wheat bread loaves sold.
Let’s represent the number of white bread loaves as “w” and the number of whole wheat bread loaves as “ww.”
1) Write a system of linear equations to represent the given information.
2) Solve the system of equations to find the number of white bread loaves and whole wheat bread loaves sold in a week.
3) Calculate the percentage of white bread loaves sold out of the total number of loaves sold.
4) If the bakery wants to increase the percentage of white bread sales to 70%, how many more white bread loaves should they sell?
5) Discuss the implications of the solution in terms of the bakery’s production and marketing strategies.
Real-world application:
This problem simulates a real-world scenario where a bakery needs to analyze their bread sales and make informed decisions based on the data. By solving the system of linear equations, students can determine the exact number of white bread and whole wheat bread loaves sold, allowing the bakery to adjust their production accordingly.
The problem also introduces the concept of percentages, as students calculate the percentage of white bread sales out of the total. This helps students understand the importance of analyzing sales data and setting goals for increasing specific product sales.
Furthermore, the problem encourages critical thinking by asking students to discuss the implications of the solution. This prompts students to consider the bakery’s production and marketing strategies, such as increasing white bread production or implementing targeted marketing campaigns to achieve the desired sales percentage.