Hector Spent $\frac{3}{4}$ Of His Money The Day After He Cashed His Paycheck Of $\$50$. Let $m$ Represent The Amount Of Money Hector Spent.Which Equation Matches The Word Problem?How Much Money Did Hector Spend?

Introduction

In this article, we will explore a mathematical problem involving Hector's money spent. We will analyze the given information, identify the key elements, and create an equation to represent the situation. Additionally, we will solve for the amount of money Hector spent.

Understanding the Problem

Hector cashed his paycheck of $\$50$ and spent $\frac{3}{4}$ of his money the day after. We need to find the amount of money Hector spent, represented by $m$. To do this, we will create an equation based on the given information.

Creating the Equation

Let's break down the information:

• Hector's paycheck is $\$50$.
• He spent $\frac{3}{4}$ of his money.
• We need to find the amount of money Hector spent, represented by $m$.

We can create an equation using the following steps:

1. Multiply Hector's paycheck by $\frac{3}{4}$ to find the amount of money he spent.
2. Set up an equation to represent the situation.

The equation can be written as:

$$m = \frac{3}{4} \times 50$$

Simplifying the Equation

To simplify the equation, we can multiply $\frac{3}{4}$ by $50$:

$$m = \frac{3}{4} \times 50 = \frac{150}{4} = 37.5$$

Conclusion

Hector spent $\$37.50$ of his money the day after he cashed his paycheck of $\$50$. The equation $m = \frac{3}{4} \times 50$ represents the situation and can be used to find the amount of money Hector spent.

Key Takeaways

• Hector's paycheck is $\$50$.
• He spent $\frac{3}{4}$ of his money.
• The equation $m = \frac{3}{4} \times 50$ represents the situation.
• Hector spent $\$37.50$ of his money.

Real-World Applications

This problem can be applied to real-life situations where an individual needs to calculate the amount of money spent based on a percentage of their income. For example, if an employee receives a paycheck of $\$1000$ and spends $\frac{2}{5}$ of it, they can use the equation $m = \frac{2}{5} \times 1000$ to find the amount of money spent.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Fractions: $\frac{3}{4}$ and $\frac{2}{5}$
• Multiplication: $\frac{3}{4} \times 50$ and $\frac{2}{5} \times 1000$
• Equations: $m = \frac{3}{4} \times 50$ and $m = \frac{2}{5} \times 1000$

Practice Problems

1. If an employee receives a paycheck of $\$800$ and spends $\frac{1}{3}$ of it, how much money did they spend?
2. If a person has $\$1200$ and spends $\frac{2}{3}$ of it, how much money did they spend?

Answer Key

1. $m = \frac{1}{3} \times 800 = \frac{800}{3} = 266.67$
2. $m = \frac{2}{3} \times 1200 = \frac{2400}{3} = 800$
   Hector's Money Spent: A Mathematical Problem - Q&A =====================================================

Introduction

In our previous article, we explored a mathematical problem involving Hector's money spent. We created an equation to represent the situation and solved for the amount of money Hector spent. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the equation that represents the situation?

A: The equation that represents the situation is $m = \frac{3}{4} \times 50$.

Q: How much money did Hector spend?

A: Hector spent $\$37.50$ of his money the day after he cashed his paycheck of $\$50$.

Q: What is the percentage of money Hector spent?

A: Hector spent $\frac{3}{4}$ of his money, which is equivalent to $75\%$.

Q: If Hector had a paycheck of $\$100$, how much money would he spend?

A: If Hector had a paycheck of $\$100$, he would spend $\frac{3}{4} \times 100 = 75$ dollars.

Q: Can I use this equation to find the amount of money spent if I have a different percentage?

A: Yes, you can use the equation $m = \frac{p}{100} \times x$ to find the amount of money spent if you have a different percentage, where $p$ is the percentage and $x$ is the amount of money.

Q: What if I want to find the amount of money spent if I have a different amount of money?

A: You can use the equation $m = \frac{p}{100} \times x$ to find the amount of money spent if you have a different amount of money, where $p$ is the percentage and $x$ is the amount of money.

Q: Can I use this equation to find the amount of money spent if I have a decimal percentage?

A: Yes, you can use the equation $m = p \times x$ to find the amount of money spent if you have a decimal percentage.

Q: What if I want to find the amount of money spent if I have a negative percentage?

A: You cannot use the equation $m = \frac{p}{100} \times x$ to find the amount of money spent if you have a negative percentage, as it would result in a negative value.

Conclusion

In this article, we answered some frequently asked questions related to Hector's money spent problem. We provided equations and examples to help you understand the concept and apply it to different situations.

Key Takeaways

• The equation $m = \frac{p}{100} \times x$ represents the situation.
• Hector spent $\$37.50$ of his money the day after he cashed his paycheck of $\$50$.
• You can use the equation to find the amount of money spent if you have a different percentage or amount of money.
• You cannot use the equation to find the amount of money spent if you have a negative percentage.

Real-World Applications

This problem can be applied to real-life situations where an individual needs to calculate the amount of money spent based on a percentage of their income. For example, if an employee receives a paycheck of $\$1000$ and spends $\frac{2}{5}$ of it, they can use the equation $m = \frac{2}{5} \times 1000$ to find the amount of money spent.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Fractions: $\frac{3}{4}$ and $\frac{2}{5}$
• Multiplication: $\frac{3}{4} \times 50$ and $\frac{2}{5} \times 1000$
• Equations: $m = \frac{3}{4} \times 50$ and $m = \frac{2}{5} \times 1000$
• Percentages: $75\%$ and $40\%$

Practice Problems

1. If an employee receives a paycheck of $\$800$ and spends $\frac{1}{3}$ of it, how much money did they spend?
2. If a person has $\$1200$ and spends $\frac{2}{3}$ of it, how much money did they spend?
3. If Hector had a paycheck of $\$100$ and spent $\frac{1}{4}$ of it, how much money would he spend?
4. If an employee receives a paycheck of $\$1000$ and spends $20\%$ of it, how much money did they spend?

Answer Key

1. $m = \frac{1}{3} \times 800 = \frac{800}{3} = 266.67$
2. $m = \frac{2}{3} \times 1200 = \frac{2400}{3} = 800$
3. $m = \frac{1}{4} \times 100 = 25$
4. $m = 0.20 \times 1000 = 200$