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.)

Piecewise Functions & Transformations

A few of observations from class today:

  • y = x – 2 does not create a horizontal line where y is always -2.
  • When creating inequalities for piecewise functions, be sure that you don’t have overlapping x-values.
  • Always use proper notation for piecewise functions.  Start with f(x).  Then draw the brace, then an expression.  The domain goes last.  A comma separates the function and the domain.

Please complete the Problem Set tonight for homework.  If you get stuck on problem 4, post a question on the blog, or come to class with a written question tomorrow.