SOLUTION: Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card.

Question 1090246: Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card. The Discount card costs $50 but would allow her to go to the pool for only $2 each time. The Flat Rate card costs $200 but would let her in to the pool for free all summer.
$$
a. What factors will be most important when Kate is deciding to buy the Discount card, the Flat Rate card, or neither?
b. Write an equation for each of the three scenarios. Explain your thinking.
c. Graph your equations in a graphing utility or in a calculator. What does the $\footnotesize{x}$-axis represent? What does the $\footnotesize{y}$-axis represent?
d. What do the intersection points of the lines represent?
e. Decide which plan you think is the best and explain why.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card. The Discount card costs $50 but would allow her to go to the pool for only $2 each time. The Flat Rate card costs $200 but would let her in to the pool for free all summer.
$$
a. What factors will be most important when Kate is deciding to buy the Discount card, the Flat Rate card, or neither?
How many times will she be going to the pool this summer.
:
b. Write an equation for each of the three scenarios. Explain your thinking.
let t = no. of time she went to the pool
f(t) = the total cost for the summer
f(t) = 5t; no card
f(t) = 2t + 50, discount card
f(t) = 200, flat rate card
:
c. Graph your equations in a graphing utility or in a calculator. What does the $\footnotesize{x}$-axis represent? What does the $\footnotesize{y}$-axis represent?
vertical axis = total cost
horizontal axis = no. of pool visits

f(t) = 5t; red
f(t) = 2t+50; green
f(t) = 200; blue
:
d. What do the intersection points of the lines represent?
At the intersections, the no. of visits the cost is the same
At 16 visits, the no card and discount card cost $80 & $82$
At 17+ visits, the discount card is a better deal, $85 & $84
and
At 40 visits, no card (40*5) and flat rate are the same.
After 40 the flat rate is a far better deal
:
e. Decide which plan you think is the best and explain why.
If you are determined to become a much better swimmer, and have the $,
take the flat rate. An added incentive to go often to get your money's worth.
:
Did all this make sense to you? A good problem to think about, don't you think? CK
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