Solving a Mathematical Word Problem: Clarifying the Correct Answer

Recently, I came across a math word problem in a video that sparked some confusion regarding the answer. The question pertained to determining the initial amount of money someone had, given certain expenditures. In this article, we will dissect the problem, analyze the solution, and provide clarity on the correct answer. Additionally, we will explore alternative interpretations to shed light on the nuances involved.

Understanding the Problem

The problem in question states:

“Found this word problem in a math video and I can’t figure out whether the answer is 180 or 140.”

The original problem provided the following details:

Let x denote the money Hone initially had.

The equation given is:

x 2/5 x 1/4 x 63

A detailed solution provided the following steps:

Mathematical Analysis of the Problem

Based on the given equation, let's break down the solution step-by-step:

Step 1: Simplifying the Equation

x 2/5 x 1/4 x 63

Converting the multipliers to a common denominator:

x 8x/20 x 5x/20 x 1260/20

Combining the terms:

x (8x 5x 1260) / 20

Step 2: Multiplying by 20

2 8x 5x 1260

2 13x 1260

2 - 13x 1260

7x 1260

x 1260 / 7 180

This confirms that the initial amount Hone had was 180.

Conclusion

In conclusion, the correct answer to the word problem is that Hone initially had 180.

Proof:

Food: 180 x 2/5 72

Clothes: 180 x 1/4 45

180 - 72 - 45 180 - 117 63 remaining.

Alternative Interpretations

Despite the clear and logical solution provided above, there are alternative interpretations of the problem, which can lead to other answers:

Interpretation 1: Separate Fractions Refer to Balance

If the fractions refer to amounts based on the balance at hand:

Paid for food: 56 (140 x 2/5)

Balance remaining before clothes: 84

Paid for clothes: 21 (84 x 1/4)

Remaining balance after clothes: 63

Thus, if he initially had 140, there would be a balance remaining of 63 after these expenditures.

Interpretation 2: Separate Fractions for Initial Amount

If the fractions refer to separate initial portions:

Paid for clothes: 35 (140 x 1/4)

Balance remaining before food: 105

Paid for food: 42 (105 x 2/5)

Remaining balance after food: 63

Thus, if he initially had 140 and these fractions were applied separately, the remaining balance would also be 63.

Summary

In summary, the mathematical problem clarifies that the initial amount Hone had was 180. However, the problem's wording can lead to different interpretations, which would result in different solutions (140 or 180). The key takeaway is to ensure clarity in problem statements to avoid ambiguity.

If you have more complex mathematical problems or need further clarification, feel free to ask in the comments section below.