Solving a Mathematical Word Problem on Mixing Peanuts and Walnuts: A Cost-Effective Guide

Let's dive into a practical mathematical problem that many of us might face in real-life situations—mixing different types of nuts to create a specific mixture with a desired price per pound. In this case, we're dealing with a grocer who stocks peanuts for $3.75 per pound and walnuts for $2.75 per pound. Our task is to mix the two to obtain a 40-pound mixture that we can sell for $3.00 per pound. But let's first break down the steps to solve this problem!

Understanding the Problem

First, we need to understand the basic principles involved in solving the problem. We are asked to mix peanuts and walnuts to achieve a 40-pound mixture that can be sold at $3.00 per pound. We have the following costs:

Peanuts: $3.75 per pound Walnuts: $2.75 per pound

Our goal is to find the correct amounts of each type of nut to achieve the desired mixture.

The Quick Mental Calculation

Here’s a quick way to calculate this problem in your head:

If we only use walnuts, the total cost for 40 pounds would be 40 * $2.75 $110.00. However, we need the mixture to sell for $3.00 per pound, which means the total cost should be 40 * $3.00 $120.00. The difference between these two amounts is $120.00 - $110.00 $10.00, which means we need to add $10.00 to the cost. The price difference per pound between peanuts and walnuts is $3.75 - $2.75 $1.00. Therefore, we need to add the more expensive peanuts to make up the difference. We need 10 pounds of peanuts to add to the walnuts to achieve the desired cost of $3.00 per pound.

This quick calculation shows us that to achieve the desired price, we need to mix 30 pounds of walnuts and 10 pounds of peanuts.

Why This Approach Works

The key to this approach lies in understanding the cost difference per pound and how it affects the overall cost of the mixture. By recognizing that the price difference per pound is $1.00, we can determine how many pounds of the more expensive peanuts we need to add to balance the cost to $3.00 per pound.

Conclusion for Real-Life Application

While the calculation is straightforward, it’s important to note that in real-life situations, businesses often want to make some profit. Thus, using the exact calculation without any profit margin is less common. However, this approach can be a powerful tool for understanding and solving similar problems in cost and mixture calculations.

If you want to practice more such problems, visit our practice section and learn more about solving mathematical word problems and applying them in real-life situations.

Related Keywords

math word problem, mixture problem, cost optimization

Real-Life Application and Further Practice

In addition to the specific problem presented, there are many scenarios where similar calculations can be applied, such as:

Diluting solutions in chemistry Blending different media types in content creation Calculating nutritional values of different food combinations

Whether you are a business owner, a student, or simply someone who enjoys solving puzzles, understanding these concepts can help you make informed decisions and solve real-world problems more effectively.

Practice Questions

Here are some similar practice questions to help you master these concepts:

How many pounds of chocolate that costs $5.00 per pound should be mixed with 30 pounds of caramel that costs $3.50 per pound to create a 50-pound mixture that sells for $4.00 per pound? A juice blend is made by mixing apples that cost $1.25 per pound with oranges that cost $1.50 per pound. How many pounds of each fruit are needed to create a 15-pound mixture that sells for $1.30 per pound?

Feel free to try these practice questions and challenge yourself. Happy problem-solving!