Sequences and Equations 01/16

Today in class we practiced writing equations for number patterns using sequence notation.

Over the weekend, please complete the problem set from lesson 27.  (That’s what you were working on in class.)

When writing equations, be sure to include all 3 important pieces of information needed to describe the pattern:  Initial value, starting point for i, and equation.

Per a student’s request, here is a link to Stanford University’s MLK Project:  http://mlk-kpp01.stanford.edu/

The True Cost of Cell Phone Ownership

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.  There are many others out there, if you find one, add it to our list!

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.

  1. Pick a phone:  Research phones at providers websites (sprint, tmobile, att, verizizon) 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
  2. Pick 2 providers:  Pre-Paid and Post-Paid.  Try to find plans that are as close to the same as possible.
  3. Use linear equations, graphs, and tables to determine your total cost over 2 years.
  4. 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 Friday, January 9.

Cell Phone Rubric

Special Systems 1/5/15

Today in class we learned that not all systems of linear equations have one solution.  Sometimes they have infinite or NO solutions.

Tonight, please determine how many solutions each system has.  You do not need to solve each problem, but you should explain briefly how you came to that conclusion!

Screen Shot 2015-01-05 at 11.03.10 AM

Substitution (and Elimination)

Today in class we learned a new method for solving linear systems of equations:  The Combination (or Elimination) Method.  Thanks Marvin!

While working on your homework tonight, you do not ALWAYS need to use this new method.  If a problem looks easier to solve using substitution, then use that instead!

7.3)  6 – 8, 12 – 14, 19 – 33, 35, 40, 42, 43.

Systems of Equations: Story Problem Edition (last night)

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.  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?

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

 

Systems of Equations and Story Problems

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.)