You Have Saved $40 So Far In Your Bank To Buy A New Pair Of Shoes. You Earn $15.25 An Hour Working At A Gas Station.Write And Solve An Inequality To Find How Many Hours You Must Work To Earn At Least $260 To Purchase The Shoes.A. You Must

Feb 27, 2025 by ADMIN 241 views

You have saved $40 so far in your bank to buy a new pair of shoes. You earn $15.25 an hour working at a gas station. Write and solve an inequality to find how many hours you must work to earn at least $260 to purchase the shoes.

A. You must

Problem Explanation

You have saved $40 and you want to buy a new pair of shoes that costs $260. You earn $15.25 per hour working at a gas station. To find out how many hours you need to work to earn at least $260, we need to set up an inequality.

Step 1: Define the variables

Let's define the variables:

x = number of hours you need to work
y = total amount of money you earn
c = cost of the shoes ($260)
s = amount of money you have saved ($40)
r = hourly wage ($15.25)

Step 2: Set up the inequality

Since you want to earn at least $260, the total amount of money you earn (y) must be greater than or equal to the cost of the shoes (c) minus the amount of money you have saved (s). We can set up the inequality as follows:

y ≥ c - s

Substituting the values, we get:

y ≥ 260 - 40 y ≥ 220

Since you earn $15.25 per hour, the total amount of money you earn (y) is equal to the number of hours you work (x) multiplied by your hourly wage (r). We can set up the equation as follows:

y = xr

Substituting the values, we get:

y = 15.25x

Step 3: Substitute the equation into the inequality

Now, we can substitute the equation y = 15.25x into the inequality y ≥ 220:

15.25x ≥ 220

Step 4: Solve the inequality

To solve the inequality, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 15.25:

x ≥ 220 / 15.25 x ≥ 14.4

Conclusion

You must work at least 14.4 hours to earn at least $260 to purchase the shoes.

Solution Explanation

The solution to the inequality is x ≥ 14.4, which means you need to work at least 14.4 hours to earn at least $260. This is because the inequality states that the total amount of money you earn (y) must be greater than or equal to the cost of the shoes (c) minus the amount of money you have saved (s).

Step 5: Check the solution

To check the solution, we can plug in x = 14.4 into the equation y = 15.25x:

y = 15.25(14.4) y = 220

Since y = 220 is greater than or equal to the cost of the shoes (c) minus the amount of money you have saved (s), the solution x ≥ 14.4 is correct.

Final Answer

The final answer is x ≥ 14.4.
You have saved $40 so far in your bank to buy a new pair of shoes. You earn $15.25 an hour working at a gas station. Write and solve an inequality to find how many hours you must work to earn at least $260 to purchase the shoes.

A. You must

Problem Explanation

Step 1: Define the variables

Let's define the variables:

x = number of hours you need to work
y = total amount of money you earn
c = cost of the shoes ($260)
s = amount of money you have saved ($40)
r = hourly wage ($15.25)

Step 2: Set up the inequality

y ≥ c - s

Substituting the values, we get:

y ≥ 260 - 40 y ≥ 220

Since you earn $15.25 per hour, the total amount of money you earn (y) is equal to the number of hours you work (x) multiplied by your hourly wage (r). We can set up the equation as follows:

y = xr

Substituting the values, we get:

y = 15.25x

Step 3: Substitute the equation into the inequality

Now, we can substitute the equation y = 15.25x into the inequality y ≥ 220:

15.25x ≥ 220

Step 4: Solve the inequality

To solve the inequality, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 15.25:

x ≥ 220 / 15.25 x ≥ 14.4

Conclusion

You must work at least 14.4 hours to earn at least $260 to purchase the shoes.

Solution Explanation

Step 5: Check the solution

To check the solution, we can plug in x = 14.4 into the equation y = 15.25x:

y = 15.25(14.4) y = 220

Since y = 220 is greater than or equal to the cost of the shoes (c) minus the amount of money you have saved (s), the solution x ≥ 14.4 is correct.

Final Answer

The final answer is x ≥ 14.4.

Q&A

Q: What is the cost of the shoes?

A: The cost of the shoes is $260.

Q: How much money have you saved?

A: You have saved $40.

Q: How much do you earn per hour?

A: You earn $15.25 per hour.

Q: What is the inequality that represents the situation?

A: The inequality is y ≥ 220, where y is the total amount of money you earn and 220 is the cost of the shoes minus the amount of money you have saved.

Q: How do you solve the inequality?

A: To solve the inequality, you need to isolate the variable x by dividing both sides of the inequality by 15.25.

Q: What is the solution to the inequality?

A: The solution to the inequality is x ≥ 14.4, which means you need to work at least 14.4 hours to earn at least $260.

Q: How do you check the solution?

A: To check the solution, you can plug in x = 14.4 into the equation y = 15.25x and verify that y is greater than or equal to the cost of the shoes minus the amount of money you have saved.

Q: What is the final answer?

A: The final answer is x ≥ 14.4.

Q: What does the solution mean?

A: The solution means that you need to work at least 14.4 hours to earn at least $260 to purchase the shoes.

Q: What if you want to earn more than $260?

A: If you want to earn more than $260, you can simply add the additional amount to the cost of the shoes and solve the inequality again.

Q: What if you want to earn less than $260?

A: If you want to earn less than $260, you can simply subtract the additional amount from the cost of the shoes and solve the inequality again.

Q: Can you use this method to solve other inequalities?

A: Yes, you can use this method to solve other inequalities by following the same steps: define the variables, set up the inequality, substitute the equation into the inequality, solve the inequality, and check the solution.