Today in class we completed our introduction of recursive and explicit equations.

Over the holiday weekend, please complete the Problem Set for Lesson 1 of your big packet!

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Today in class we completed our introduction of recursive and explicit equations.

Over the holiday weekend, please complete the Problem Set for Lesson 1 of your big packet!

Today in class we reviewed the notation and language associated with sequences and recursion.

Tonight, please create equations (all 3 parts) for the following sequences:

- 9, 13, 17, 21 (plus four pattern)
- 1, 5, 25, 125 (times five pattern)
- -5, -8, -11, -14 (minus 3 pattern)

Most of us use “Post Paid” plans for cell phones. Verizon, AT&T, Sprint, & T-Mobile are the four largest cell phone providers in the US. With any of these providers you buy your phone at a discounted price, but (typically) agree to a 2 year contract.

There are also a lot of “Pre Paid” cell phone providers. With this service, you do NOT have a contract. You also have to pay the full price for your phone. Boost Mobile, Virgin Mobile, Simple Mobile, and Straight Talk are just a few of the prepaid providers. Recently Google created their own program called “Google Fi”.

Your goal is to determine whether it is best to use a pre-paid or post-paid cell phone plan when comparing a 2 year time period.

- Pick a phone: Research phones at providers websites (sprint, tmobile, att, verizon) or discounters (like wireless.amazon.com). Pick the phone you really want. Non contract phones can be found at: newegg.com, play.google.com, wireless.amazon.com
- Pick 2 providers: Try to find plans that are as close to the same as possible.
- Use linear equations, graphs, and tables to determine your total cost over 2 years.
- Create a summary report. The report should include the following topics:
- After how many months do both plans have the same value.
- Over 2 years, which is the better value? (By how much?)
- How much cash “up front” do you need to get started?
- Which plan and phone would you pick and why?
- The report should be in paragraph form.
**Due at the end of class on Wednesday, November 18.**

These are all considered “classic” story problems. Please create equations and solve 3 of the problems below:

1. During the spring and summer, you do a spring yard cleanup for households and you also paint houses. You earn $8 an hour doing cleanups and $12 an hour painting. Last spring and summer, you worked a total of 400 hours and earned $3800. How many hours did you spend doing yard cleanups? How many hours did you spend painting?

2. A total of $45,000 is invested into two funds paying 5.5% and 6.5% annual interest. The combined annual interest is $2725. How much of the $45,000 is invested in each type of fund?

3. Read the following article at the New York Times. How many people downloaded the video and how many purchased it?

4. Two swimming teams are competing in a 400 meter relay. Each leg of the relay is 100 meters. During the last leg of the race, the swimmer in lane 1 has a 1.2 second head start on the swimmer in lane 2 as shown. After how many seconds into the leg will the swimmer in lane 2 catch up to the swimmer in lane 1.

5. In your chemistry lab, you have a bottle of 1% hydrochloric acid solution and a bottle of 5% hydrochloric acid solution. You need 100 milliliters of a 3% hydrochloric acid solution for an experiment. How many milliliters of each solution do you need to mix together?

6. A rectangle has a perimeter of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Find the length and width of the rectangle

Please pick 3 of the problems below.

- Create equations to represent the situation.
- Explain in words how the equation fits each part of the problem.
- Solve the system of equations.

1. A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at 9% and how much is invested at 11%?

2. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?

3. Larry wants 50 pounds of tea that ha can sell for $5.14 per pound. If he has tea that costs $7.80 per pound and tea that costs $4.30 per pound, how much of each should he use?

4. Kerry’s motorboat takes 3 hours to make a downstream trip with a 3-mph current. The return trip against the same current takes 5 hours. Find the speed of the boat in still water.

5. The Hare knows he can run faster than the Tortoise, so he gave the Tortoise a 2 mile head start. The Hare usually runs about 6 miles per hour while the Tortoise can hold a sustained 3 miles per hour all day long.” Find and explain the meaning of the solution to this linear system.

6. There are 2 times as many quarters as dimes in Eric’s pocket. He has $1.20 in coins totally. How many coins of each type does Eric have?

**Challenge Problem (Optional): ** In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have? (Try solving this problem without guess and check.)

Today in class we learned how to find a solution to a System of Equations using the Elimination (Combination) method.

Tonight, please complete Exercises 1 – 3 and Problem Set 1 – 3 in Lesson 28.

Please work on this today and over the weekend!

Please complete through Problem 4 (in the Classwork Section) for class on Monday.

Today in class we continued our study of Standard Form.

Tonight, complete the Problem Set from lesson 12.

For the three problems below, create an equation that could model the situation. When is it easier to use Standard Form? Why?

- A gardener is choosing flowers for his new garden. Vinca costs $1.20 per plant. Phlox costs $2.50 per plant. He has $300 to spend in total.
- A snack mix requires 120 oz of some corn cereal and some wheat cereal. Corn cereal comes in 12 oz boxes. The last time you made the mix, you used 5 boxes of corn cereal and 4 boxes of wheat cereal.
- In order to use an excerpt from a movie in a new television show, the television producer must pay the director of the movie $790 for the first 2 minutes of the excerpt and $130 per minute after that.
- Create a situation that could be modeled by an equation in Standard Form. Write the story and explain how the equation fits the situation.

Please try these problems from Chapter 5 of the old “Kayak” book over the weekend. They are much more “traditional” (boring) than what we typically do, but I thought it would be good practice.

We will have a test over Linear Functions on Thursday of next week.