Ezra Works Two Summer Jobs To Save For A Laptop That Costs At Least $ \$1100 $. He Charges $ \$15 $ Per Hour To Mow Lawns And $ \$10 $ Per Hour To Walk Dogs. He Currently Charges In Half-hour Intervals.The Inequality

Feb 27, 2025 by ADMIN 217 views

Ezra's Summer Jobs: A Math Problem

Ezra is a hardworking individual who has taken on two summer jobs to save up for a laptop that costs at least $1100. He earns money by mowing lawns and walking dogs, charging $15 per hour for the former and $10 per hour for the latter. However, he currently charges in half-hour intervals, which can make it difficult to calculate his total earnings. In this article, we will explore the math behind Ezra's summer jobs and determine how much he needs to work to reach his goal.

Let's start by setting up an inequality to represent Ezra's situation. We know that he charges $15 per hour to mow lawns and $10 per hour to walk dogs. Since he charges in half-hour intervals, we can assume that he works for 0.5 hours (or 30 minutes) at a time. We also know that he wants to save up at least $1100 for the laptop.

Let x be the number of hours Ezra works mowing lawns and y be the number of hours he works walking dogs. Then, his total earnings can be represented by the inequality:

15x + 10y ≥ 1100

However, since Ezra charges in half-hour intervals, we need to multiply the number of hours he works by 2 to get the total number of half-hour intervals. This gives us:

30x + 20y ≥ 1100

To simplify the inequality, we can divide both sides by 10:

3x + 2y ≥ 110

This inequality represents the minimum number of hours Ezra needs to work to reach his goal of saving up at least $1100 for the laptop.

To visualize the inequality, we can graph it on a coordinate plane. The x-axis represents the number of hours Ezra works mowing lawns, and the y-axis represents the number of hours he works walking dogs. The inequality 3x + 2y ≥ 110 represents a line on the coordinate plane, and all the points above this line satisfy the inequality.

To find the solution to the inequality, we need to find the values of x and y that satisfy the inequality. We can do this by finding the intersection point of the line 3x + 2y = 110 and the x-axis. This gives us the point (37, 0), which represents the minimum number of hours Ezra needs to work mowing lawns to reach his goal.

Similarly, we can find the intersection point of the line 3x + 2y = 110 and the y-axis. This gives us the point (0, 55), which represents the minimum number of hours Ezra needs to work walking dogs to reach his goal.

In conclusion, Ezra's summer jobs can be represented by the inequality 3x + 2y ≥ 110, where x is the number of hours he works mowing lawns and y is the number of hours he works walking dogs. By graphing the inequality on a coordinate plane, we can visualize the solution and find the minimum number of hours Ezra needs to work to reach his goal of saving up at least $1100 for the laptop.

The math behind Ezra's summer jobs has real-world applications in many areas, including finance, economics, and business. For example, a company may use similar calculations to determine the minimum number of hours an employee needs to work to reach a certain sales goal. Similarly, a financial advisor may use similar calculations to determine the minimum amount of money an individual needs to save to reach a certain financial goal.

Based on the math behind Ezra's summer jobs, here are some tips for him to reach his goal:

Work efficiently: To maximize his earnings, Ezra should work efficiently and complete his tasks as quickly as possible.
Charge for half-hour intervals: Since Ezra charges in half-hour intervals, he should make sure to charge for each half-hour interval separately.
Keep track of his earnings: Ezra should keep track of his earnings and make sure to add up his total earnings at the end of each day.
Save his earnings: Ezra should save his earnings in a separate account to avoid spending them on unnecessary items.

By following these tips, Ezra can reach his goal of saving up at least $1100 for the laptop and achieve his financial goals.

In conclusion, the math behind Ezra's summer jobs is a complex problem that requires careful calculations and analysis. By using the inequality 3x + 2y ≥ 110, we can visualize the solution and find the minimum number of hours Ezra needs to work to reach his goal of saving up at least $1100 for the laptop. By following the tips outlined in this article, Ezra can reach his goal and achieve his financial goals.
Ezra's Summer Jobs: A Math Problem - Q&A

In our previous article, we explored the math behind Ezra's summer jobs and determined how much he needs to work to reach his goal of saving up at least $1100 for the laptop. In this article, we will answer some frequently asked questions about Ezra's summer jobs and provide additional insights into the math behind his situation.

Q: How much does Ezra need to work to reach his goal?

A: To reach his goal of saving up at least $1100 for the laptop, Ezra needs to work a minimum of 37 hours mowing lawns and 55 hours walking dogs.

Q: What if Ezra wants to save up more than $1100 for the laptop?

A: If Ezra wants to save up more than $1100 for the laptop, he will need to work more hours mowing lawns and walking dogs. We can calculate the additional hours he needs to work by adding the extra amount he wants to save to the inequality 3x + 2y ≥ 110.

Q: How can Ezra maximize his earnings?

A: To maximize his earnings, Ezra should work efficiently and complete his tasks as quickly as possible. He should also charge for each half-hour interval separately and keep track of his earnings to avoid losing any money.

Q: What if Ezra wants to work fewer hours mowing lawns and more hours walking dogs?

A: If Ezra wants to work fewer hours mowing lawns and more hours walking dogs, he can adjust the inequality 3x + 2y ≥ 110 accordingly. For example, if he wants to work 20 hours mowing lawns and 60 hours walking dogs, he can substitute these values into the inequality to get 60 ≥ 110.

Q: Can Ezra use the inequality to determine how much he needs to work to reach a specific financial goal?

A: Yes, Ezra can use the inequality to determine how much he needs to work to reach a specific financial goal. For example, if he wants to save up $1500 for a new bike, he can add $400 to the inequality 3x + 2y ≥ 110 to get 3x + 2y ≥ 210.

Q: How can Ezra use the inequality to compare his earnings to his expenses?

A: Ezra can use the inequality to compare his earnings to his expenses by setting up a second inequality that represents his expenses. For example, if his expenses are $500 per month, he can set up the inequality 3x + 2y ≤ 500 to represent his expenses.

In conclusion, the math behind Ezra's summer jobs is a complex problem that requires careful calculations and analysis. By using the inequality 3x + 2y ≥ 110, we can visualize the solution and find the minimum number of hours Ezra needs to work to reach his goal of saving up at least $1100 for the laptop. By answering the frequently asked questions outlined in this article, we can gain a deeper understanding of the math behind Ezra's situation and provide additional insights into his financial goals.

Based on the math behind Ezra's summer jobs, here are some additional tips for him to reach his goal:

Create a budget: Ezra should create a budget to track his income and expenses and make sure he is saving enough money for his financial goals.
Prioritize his goals: Ezra should prioritize his financial goals and make sure he is working towards the most important ones first.
Avoid unnecessary expenses: Ezra should avoid unnecessary expenses and make sure he is not spending too much money on non-essential items.
Save regularly: Ezra should save regularly and make sure he is setting aside a portion of his income each month.

By following these tips, Ezra can reach his goal of saving up at least $1100 for the laptop and achieve his financial goals.