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

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Introduction

In this problem, we are given that Hector spent 34\frac{3}{4} of his money the day after he cashed his paycheck of $50. We need to find the equation that matches the word problem and calculate the amount of money Hector spent.

Understanding the Problem

Let's break down the problem step by step:

  • Hector has a paycheck of $50.
  • He spends 34\frac{3}{4} of his money the day after he cashes his paycheck.
  • We need to find the amount of money Hector spent, represented by mm.

Equation Matching

To find the equation that matches the word problem, we need to translate the given information into a mathematical equation. Let's start by representing the amount of money Hector has after he cashes his paycheck as xx. Since he spends 34\frac{3}{4} of his money, the amount of money he has left is x−34xx - \frac{3}{4}x.

We can simplify this expression by combining like terms:

x−34x=14xx - \frac{3}{4}x = \frac{1}{4}x

This means that Hector has 14\frac{1}{4} of his original money left.

Calculating the Amount Spent

Now that we have the equation that matches the word problem, we can calculate the amount of money Hector spent. We know that Hector has a paycheck of $50, and he spends 34\frac{3}{4} of his money. To find the amount of money he spent, we can multiply the amount of money he has by the fraction he spends:

m=34×50m = \frac{3}{4} \times 50

To calculate this, we can multiply the numerator and denominator by 50:

m=3×504×50m = \frac{3 \times 50}{4 \times 50}

m=150200m = \frac{150}{200}

m=34×50m = \frac{3}{4} \times 50

m=37.5m = 37.5

Therefore, Hector spent $37.5 of his money.

Conclusion

In this problem, we were given that Hector spent 34\frac{3}{4} of his money the day after he cashed his paycheck of $50. We found the equation that matches the word problem and calculated the amount of money Hector spent. The equation that matches the word problem is m=34×50m = \frac{3}{4} \times 50, and the amount of money Hector spent is $37.5.

Key Takeaways

  • To find the equation that matches the word problem, we need to translate the given information into a mathematical equation.
  • We can simplify the equation by combining like terms.
  • To calculate the amount of money Hector spent, we can multiply the amount of money he has by the fraction he spends.

Practice Problems

  1. Tom has a paycheck of $60. He spends 23\frac{2}{3} of his money the day after he cashes his paycheck. How much money does Tom spend?
  2. Sarah has a paycheck of $80. She spends 12\frac{1}{2} of her money the day after she cashes her paycheck. How much money does Sarah spend?

Answer Key

  1. m=23×60=40m = \frac{2}{3} \times 60 = 40
  2. m=12×80=40m = \frac{1}{2} \times 80 = 40

References

About the Author

Q: What is the equation that matches the word problem?

A: The equation that matches the word problem is m=34×50m = \frac{3}{4} \times 50, where mm represents the amount of money Hector spent.

Q: How do I simplify the equation?

A: To simplify the equation, you can combine like terms. In this case, we can simplify the expression x−34xx - \frac{3}{4}x by combining like terms:

x−34x=14xx - \frac{3}{4}x = \frac{1}{4}x

Q: How do I calculate the amount of money Hector spent?

A: To calculate the amount of money Hector spent, you can multiply the amount of money he has by the fraction he spends:

m=34×50m = \frac{3}{4} \times 50

To calculate this, you can multiply the numerator and denominator by 50:

m=3×504×50m = \frac{3 \times 50}{4 \times 50}

m=150200m = \frac{150}{200}

m=37.5m = 37.5

Q: What if Hector had a different amount of money? How would the equation change?

A: If Hector had a different amount of money, the equation would change accordingly. For example, if Hector had a paycheck of $100, the equation would be:

m=34×100m = \frac{3}{4} \times 100

To calculate this, you can multiply the numerator and denominator by 100:

m=3×1004×100m = \frac{3 \times 100}{4 \times 100}

m=300400m = \frac{300}{400}

m=75m = 75

Q: Can I use this equation to solve other problems?

A: Yes, you can use this equation to solve other problems. For example, if you know the amount of money someone has and the fraction they spend, you can use the equation to find the amount of money they spent.

Q: What if the fraction is not a simple fraction, such as 34\frac{3}{4}? How do I handle this?

A: If the fraction is not a simple fraction, you can still use the equation to find the amount of money spent. For example, if the fraction is 25\frac{2}{5}, you can multiply the numerator and denominator by 5 to get:

m=2×55×5m = \frac{2 \times 5}{5 \times 5}

m=1025m = \frac{10}{25}

m=0.4m = 0.4

Q: Can I use this equation to solve problems with decimals?

A: Yes, you can use this equation to solve problems with decimals. For example, if Hector has a paycheck of $50 and spends 0.75 of his money, you can use the equation to find the amount of money he spent:

m=0.75×50m = 0.75 \times 50

m=37.5m = 37.5

Q: What if I have a problem with a negative fraction, such as −34-\frac{3}{4}? How do I handle this?

A: If you have a problem with a negative fraction, you can still use the equation to find the amount of money spent. For example, if Hector has a paycheck of $50 and spends −34-\frac{3}{4} of his money, you can multiply the numerator and denominator by 50:

m=−3×504×50m = -\frac{3 \times 50}{4 \times 50}

m=−150200m = -\frac{150}{200}

m=−37.5m = -37.5

Conclusion

In this Q&A article, we have covered various questions related to Hector's money problem. We have discussed how to simplify the equation, calculate the amount of money Hector spent, and handle different types of fractions and decimals. We have also provided examples of how to use the equation to solve other problems.