Solving Math Problems: How Much Food is Left After Consumption and Donation?

Introduction

Math problems can be tricky, especially when dealing with fractions and the relationships between parts of a whole. This article will guide you through solving a specific problem involving food consumption and donation, alongside a detailed explanation to help you understand the process.

Understanding the Problem

The initial scenario presented is as follows: 'Phil went to the store to pick up food and paid 47 for it. He then ate 1/12 of the food and gave 7/10 of the remaining food to his mom. What is the value of the food he has left?'

Step-by-Step Solution

Option 1: Math Problem - Simplified Method

In the first solution, the math problem is broken down into clear steps:

Phil ate 1/12 of the food. Phil gave 7/10 of the remaining food to his mom. Finally, he has the food remaining.

The key is to calculate the remaining food after these actions. First, we need to find out how much of the food was left after Phil ate 1/12 of it. This leaves 1 - 1/12 11/12 of the food.

1 - 1/12 11/12

Next, he gave 7/10 of the remaining 11/12 to his mom. We calculate 7/10 of 11/12:

7/10 * 11/12 77/120

So, the remaining food after giving to his mom is:

11/12 - 77/120 (110 - 77) / 120 33/120 11/40

This simplifies to 11/40, which is the fraction of the original amount of food that is remaining. However, the initial provided steps suggest a simpler method is also valid, where:

1 - 22/60 (60/60 - 22/60) 38/60

This reduces to 19/30, which is the fraction of the original amount of food that he has left.

Option 2: Simplified Calculation

Another view presents a simplified calculation. According to this approach, the sum of the fractions 1/12 and 7/10 is 47/60. This indicates that the remaining fraction is 1 - 47/60 13/60.

1 - 47/60 13/60

So, the food remaining is 13/60 of the original amount. To find the value of this remaining food, multiply 47 (the cost of the food) by 13/60:

47 * 13/60 611/60 ≈ 10.18

This approximately equals 10.18, which is the value of the food he has left.

Other Interpretations

The problem can be interpreted differently. The fourth suggestion considers the view that he gave 2/10 of the original food before eating 1/6 of the 8/10 left. This leaves 8/10 - 2/10 6/10, and then 1/6 of 6/10, which gives 6/10 - 1/6*6/10 10/10 - 1/10 9/10.

The fifth suggestion simplifies to 1/10 of the food, indicating 4.70 worth of food.

Conclusion

The correct interpretation and solution usually involve converting fractions to a common denominator and then performing the arithmetic. The problem can have different interpretations based on the order and quantity of the fractions given. The key is to ensure that the fractions are simplified and that the remaining fraction is calculated accurately.

Keywords: math problem, fraction calculation, food calculation