Ezra Works Two Summer Jobs To Save For A Laptop That Costs At Least $\$1100$. He Considers Adjusting His Rates To The Following:- Lawn Care: $\$250$ Per Lawn For The Summer- Dog Walking: $\$300$ Per Dog For The SummerWhich

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Introduction

Ezra is a hardworking individual who has taken on two summer jobs to save up for a laptop that costs at least $1100\$1100. He is considering adjusting his rates for lawn care and dog walking to increase his earnings. In this article, we will explore the math behind Ezra's decision and determine whether adjusting his rates will help him reach his goal.

Ezra's Current Earnings

Let's assume that Ezra currently earns $x\$x per lawn for lawn care and $y\$y per dog for dog walking. We can represent his total earnings for the summer as the sum of his earnings from both jobs:

Total Earnings=x×Number of Lawns+y×Number of Dogs\text{Total Earnings} = x \times \text{Number of Lawns} + y \times \text{Number of Dogs}

We are given that Ezra is considering adjusting his rates to $250\$250 per lawn for lawn care and $300\$300 per dog for dog walking. We can represent his new earnings as:

New Earnings=250×Number of Lawns+300×Number of Dogs\text{New Earnings} = 250 \times \text{Number of Lawns} + 300 \times \text{Number of Dogs}

The Problem

Ezra wants to know whether adjusting his rates will help him reach his goal of saving up for a laptop that costs at least $1100\$1100. We can represent this as an inequality:

New Earnings≥1100\text{New Earnings} \geq 1100

Substituting the expression for New Earnings, we get:

250×Number of Lawns+300×Number of Dogs≥1100250 \times \text{Number of Lawns} + 300 \times \text{Number of Dogs} \geq 1100

Solving the Inequality

To solve this inequality, we can start by isolating the term involving the number of lawns:

250×Number of Lawns≥1100−300×Number of Dogs250 \times \text{Number of Lawns} \geq 1100 - 300 \times \text{Number of Dogs}

Dividing both sides by 250, we get:

Number of Lawns≥1100−300×Number of Dogs250\text{Number of Lawns} \geq \frac{1100 - 300 \times \text{Number of Dogs}}{250}

Interpreting the Results

The inequality tells us that the number of lawns Ezra needs to mow must be greater than or equal to the expression on the right-hand side. This means that if Ezra wants to reach his goal of saving up for a laptop, he must mow a certain number of lawns, depending on the number of dogs he walks.

For example, if Ezra walks 2 dogs, the inequality becomes:

Number of Lawns≥1100−300×2250\text{Number of Lawns} \geq \frac{1100 - 300 \times 2}{250}

Simplifying, we get:

Number of Lawns≥1100−600250\text{Number of Lawns} \geq \frac{1100 - 600}{250}

Number of Lawns≥500250\text{Number of Lawns} \geq \frac{500}{250}

Number of Lawns≥2\text{Number of Lawns} \geq 2

This means that if Ezra walks 2 dogs, he must mow at least 2 lawns to reach his goal.

Conclusion

In conclusion, adjusting Ezra's rates to $250\$250 per lawn for lawn care and $300\$300 per dog for dog walking will help him reach his goal of saving up for a laptop, but only if he mows a certain number of lawns, depending on the number of dogs he walks. By understanding the math behind Ezra's decision, we can see that adjusting his rates is a viable option for increasing his earnings and reaching his goal.

Recommendations

Based on our analysis, we recommend that Ezra consider the following:

  • Adjust his rates to $250\$250 per lawn for lawn care and $300\$300 per dog for dog walking.
  • Determine the number of lawns he needs to mow, depending on the number of dogs he walks.
  • Make sure to mow at least the required number of lawns to reach his goal.

Introduction

In our previous article, we explored the math behind Ezra's decision to adjust his rates for lawn care and dog walking to increase his earnings. We determined that adjusting his rates to $250\$250 per lawn for lawn care and $300\$300 per dog for dog walking will help him reach his goal of saving up for a laptop, but only if he mows a certain number of lawns, depending on the number of dogs he walks.

In this article, we will answer some frequently asked questions about Ezra's summer jobs and provide additional insights into the math behind his decision.

Q&A

Q: How many lawns does Ezra need to mow to reach his goal?

A: The number of lawns Ezra needs to mow depends on the number of dogs he walks. If he walks 2 dogs, he needs to mow at least 2 lawns. If he walks 3 dogs, he needs to mow at least 3 lawns, and so on.

Q: What if Ezra wants to walk more dogs?

A: If Ezra wants to walk more dogs, he will need to mow more lawns to reach his goal. For example, if he walks 4 dogs, he will need to mow at least 4 lawns.

Q: Can Ezra adjust his rates again?

A: Yes, Ezra can adjust his rates again if he wants to. However, he will need to recalculate the number of lawns he needs to mow to reach his goal.

Q: What if Ezra wants to save up for a more expensive laptop?

A: If Ezra wants to save up for a more expensive laptop, he will need to mow more lawns or walk more dogs to reach his goal.

Q: Can Ezra use a calculator to help him with the math?

A: Yes, Ezra can use a calculator to help him with the math. He can plug in the numbers and solve for the number of lawns he needs to mow.

Q: What if Ezra makes a mistake in his calculations?

A: If Ezra makes a mistake in his calculations, he may not reach his goal. It's essential to double-check his work to ensure he has the correct answer.

Additional Insights

  • Ezra's decision to adjust his rates is a great example of how math can be applied to real-life situations.
  • The math behind Ezra's decision is based on the concept of inequalities, which is a fundamental concept in algebra.
  • Ezra's story highlights the importance of careful planning and calculation when making financial decisions.

Conclusion

In conclusion, Ezra's summer jobs provide a great example of how math can be applied to real-life situations. By understanding the math behind his decision, we can see that adjusting his rates is a viable option for increasing his earnings and reaching his goal. We hope this Q&A article has provided additional insights into the math behind Ezra's decision and has helped readers understand the importance of careful planning and calculation when making financial decisions.

Recommendations

Based on our analysis, we recommend that readers:

  • Use math to help them make informed financial decisions.
  • Double-check their work to ensure they have the correct answer.
  • Consider the long-term implications of their financial decisions.

By following these recommendations, readers can make informed financial decisions and achieve their goals.