*I'll be reviewing a*

**New York State Regents Exam**Question every day from now until the Regents exams begin next month. At least, that is the plan.### June 2014, Questions 35

**35. ** *Caitlin has a movie rental card worth $175. After she rents the first movie, the card's value is$172.25. After she rents the second movie, its value is $169.50. After she rents the third movie, the car is worth $166.75.
Assuming the pattern continues, write an equation to define A(n), the amount of money on the rental card after n rentals.
*

*Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie using the rental card only? Explain how you arrived at your answer.*

First, **"Explain"** means *in words*; equations will NOT be enough information. I am not kidding.

Subtract 175-172.25 and you get $2.75. Check the next and the next to be sure, but you see that each rental is $2.75

That makes the equation **A(n) = -2.75n + 175**.

To answer the second part, make an inequality greater than 0, and find the largest whole number which makes it true. (Or make an equation equal to 0 and drop everything after the decimal.)

-2.75n + 175 > 0

-2.75n > -175

**n < 63.63**

Each movie costs $2.75 to rent. If you divide $175 by $2.75, you can get

**63 rentals**. There is money left over, but not enough for another rental using the card only.

At one rental per week, she can do this for **63 weeks** before she runs out of money.

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.

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