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?
I'll get you started:
a. Early Pay: y = 45.00
b. Deposit Plus: y = 20.00+2.00x
c. Daily Pay: y = 3.50x
Now, plug in your numbers, and come back if you get stuck.
ok i put the answers in.. now what
for #3, try going to
rechneronline . de/function-graphs/
and graph each function above.
For #4,5,6 take a look at your table and answer the questions. You should have a row or column for 10 days, 12 days, 14 days, etc. Look up the y-values for the given number of days.
1a. Early Pay: The cost, y, of swimming is a function of the number of days swimming, x. Since the cost is a flat rate of $45, the equation is y = $45.
1b. Deposit Plus: The cost, y, of swimming is a function of the number of days swimming, x. The equation can be written in slope-intercept form as y = mx + b, where m is the rate per day and b is the deposit. In this case, the rate per day is $2.00, so the equation is y = $2.00x + $20.
1c. Daily Pay: The cost, y, of swimming is a function of the number of days swimming, x. The equation can be written in slope-intercept form as y = mx + b, where m is the rate per day. In this case, the rate per day is $3.50, so the equation is y = $3.50x.
2. 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 | $45 | $45 | $45 | $45 | $45 |
| Deposit Plus | Cost | $20 | $40 | $44 | $48 | $60 |
| Daily Pay | Cost | $0 | $35 | $42 | $49 | $70 |
3. On your own, graph each equation on the same set of axes to visually compare the payment methods.
4. If Evan goes swimming 10 times, the best payment method for him would be the Deposit Plus method. He would have to pay $40.
5. If Evan goes swimming 12 times, the best payment method for him would still be the Deposit Plus method. He would have to pay $44.
6. If Evan goes swimming 14 times, the best payment method for him would still be the Deposit Plus method. He would have to pay $48.
7. If Evan doesn't know how many times he will go swimming, the best method for him would depend on his preferences and budget. The Daily Pay method has a lower rate per day but can add up if he swims frequently. The Deposit Plus method has a higher initial deposit but a lower rate per day, making it more cost-effective for a larger number of days swimming. The Early Pay method is a flat rate, so it may be more suitable if Evan plans to swim a lot of days and wants to pay upfront. Ultimately, Evan should choose the method that aligns with his swimming habits and budget.