Summer Swimming Selection

The municipal swimming pool in Nicetown has three different ways of paying for individual open swimming. Evan is trying to decide which way to pay.
• Early Pay: Pay $45 before Memorial Day; swim any number of days
• Deposit Plus: $20 deposit plus $2.00 per day
• Daily Pay: $3.50 per day

1. Write an equation for each situation such that the cost, y, of swimming is a function of the number of days swimming, x. The ordered pairs will be in the form, (x, y), and you can write your equations in slope-intercept form.
a. Early Pay:
b. Deposit Plus:
c. Daily Pay:

2. Fill in the table with the costs of swimming the given number of days.
Table of swimming costs using the three different payment methods
Payment Method Number of days 0 days 10 days 12 days 14 days 20 days
Early Pay
Deposit Plus
Daily Pay

3. On your own (ungraded), graph each equation on the same set of axes so you can visually compare the payment methods. Let the horizontal axis be the number of days swimming, x, and the vertical axis the cost in dollars, y.

Answer the following questions:

4. If Evan goes swimming 10 times, which is the best payment method for him, and how much will he have to pay?

5. If Evan goes swimming 12 times, which is the best method for him, and how much will he have to pay?

6. If Evan goes swimming 14 times, which is the best method for him, and how much will he have to pay?

7. If Evan doesn’t know how many times he will go swimming, which method do you think he should choose and why?

Can someone please fully explain what I need to do for this project? I really need help. Thanks guys

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OK. we have

a. Early Pay: y = 45.00
b. Deposit Plus: y = 20.00+2.00x
c. Daily Pay: y = 3.50x

Your table should look something like this:

days: 0 10 12 14 20
a. 45 45 45 45 45
b. 20 40 44 48 60
c. 0 35 42 49 70

4. for n=10, Daily is the best (35)
5. for n=12, Daily is the best (42)
6. for n=14, Early is best (45)
7. Hard to say. If he only goes occasionally, then Daily is best. If he goes more than about 13 times, Early is best.

Sure! I'll break it down for you step-by-step:

1. Write an equation for each payment method such that the cost, y, of swimming is a function of the number of days swimming, x. The ordered pairs will be in the form (x, y) and you can write your equations in slope-intercept form.

a. Early Pay:
For the early pay option, you pay a flat fee of $45 before Memorial Day and can swim any number of days. Since the cost is not dependent on the number of days swimming, the equation would be y = $45.

b. Deposit Plus:
For the deposit plus option, you pay a $20 deposit and an additional $2.00 per day. The equation would be y = $2x + $20, where x represents the number of days swimming and y represents the cost.

c. Daily Pay:
For the daily pay option, you pay $3.50 per day. The equation would be y = $3.50x, where x represents the number of days swimming and y represents the cost.

2. Fill in the table with the costs of swimming for the given number of days using the three different payment methods.
Table of swimming costs using the three different payment methods:

Payment Method Number of Days 0 days 10 days 12 days 14 days 20 days
Early Pay $45 $45 $45 $45 $45
Deposit Plus $20 deposit + $2 per day $20 $40 $44 $48 $60
Daily Pay $3.50 per day $0 $35 $42 $49 $70

3. Graph each equation on the same set of axes to visually compare the payment methods. Let the horizontal axis be the number of days swimming, x, and the vertical axis be the cost in dollars, y.

You can plot the points for each payment method (0 days, cost) (10 days, cost) (12 days, cost) (14 days, cost) and (20 days, cost) on a graph. Connect these points with a straight line for the Early Pay and Deposit Plus options. The Daily Pay option will be a straight line passing through the origin (0,0) with a slope of $3.50.

4. If Evan goes swimming 10 times, we can look at the table to determine the best payment method and how much he will have to pay.
From the table, we can see that the Deposit Plus option costs $40 for 10 days. So, the best payment method for Evan if he goes swimming 10 times would be the Deposit Plus option, and he will have to pay $40.

5. If Evan goes swimming 12 times, we can again look at the table to determine the best payment method and cost.
From the table, we can see that the Deposit Plus option costs $44 for 12 days. So, the best payment method for Evan if he goes swimming 12 times would still be the Deposit Plus option, and he will have to pay $44.

6. If Evan goes swimming 14 times, we can use the table to determine the best payment method and cost.
From the table, we can see that the Daily Pay option costs $49 for 14 days. So, the best payment method for Evan if he goes swimming 14 times would be the Daily Pay option, and he will have to pay $49.

7. If Evan doesn't know how many times he will go swimming, we can determine the best payment method based on his potential usage.
If he plans to swim fewer than 10 days, the Daily Pay option would be the cheapest. If he plans to swim between 10 and 13 days, the Deposit Plus option would be the cheapest. If he plans to swim 14 days or more, the Daily Pay option would be the cheapest. Therefore, if Evan doesn't know how many times he will go swimming, he should choose the Deposit Plus payment method because it offers flexibility for a range of days and would be the most cost-effective for him overall.

I hope this clarifies the steps you need to follow for the project. Let me know if you have any further questions!

Sure! I'll guide you through each step of the project.

1. Writing equations:
To write an equation for each situation, we need to determine the cost, y, of swimming as a function of the number of days swimming, x. Let's write the equations in slope-intercept form.

a. Early Pay:
The cost is a fixed amount of $45, regardless of the number of days swimming. So the equation for early pay is y = $45.

b. Deposit Plus:
The cost includes a $20 deposit plus an additional $2.00 per day. The equation for deposit plus is y = $20 + $2.00x.

c. Daily Pay:
The cost is $3.50 per day. The equation for daily pay is y = $3.50x.

2. Filling in the table:
Now, let's fill in the table with the costs of swimming for each payment method.
Table of swimming costs using the three different payment methods:

Payment Method Number of days 0 days 10 days 12 days 14 days 20 days
Early Pay Cost ($)

Deposit Plus Cost ($)

Daily Pay Cost ($)

To find the costs for each method, substitute the number of days into the corresponding equations and calculate the values.

3. Graphing the equations:
To visually compare the payment methods, plot the equations on the same set of axes. Take the horizontal (x) axis as the number of days swimming and the vertical (y) axis as the cost in dollars. Plot the points using the calculated values from the table.

4. Deciding the best payment method for Evan:
To determine the best payment method for Evan, consider the cost for a specific number of days swimming.

a. If Evan goes swimming 10 times, compare the costs under each payment method and choose the lowest cost.

b. Repeat the same process for Evan going swimming 12 and 14 times.

c. If Evan doesn't know the exact number of times he will go swimming, compare the costs under each payment method for different numbers of days and select the payment method with the lowest cost.

That's it! By following these steps, you should be able to complete the project. If you have any further questions or need assistance, feel free to ask.