05 - 06. Systems of Equations

Intro Question: nim

• What does it mean to analyze a situation? To 'solve' a situation?

Systems of Equations:

• Why do we create them?

• Can have zero, one, infinite amounts of solutions

  • parallel

  • intersection

  • same line

Question One: What allows us to have those solutions?

Question Two: A matter of tickets.

At a recent event, adults cost $7.50, children $4.00. The total amount of income was 3312.50 off the 500 tickets sold. In this completely made up scenario, how many of each type of ticket were sold?

Question Three: I've got a problem and am looking for a solution.

You want 10 liters of a 15% solution, and how have limitless amounts of 10% solution and 30% solution. How much of each do we need?

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Here's two pictures: how many pumpkins are in the jar? How did you arrive at the answer?

Question Four: The Farm

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

Question Five: Candy Contrivance

Calvin mixes candy that sells for $2.00 per pound with candy that costs $3.60 per pound to make 50 pounds of candy selling for $2.16 per pound. How many pounds of each kind of candy did he use in the mix?

Question Six: Car Decisions

Car 1: 2012 Ford Fiesta. $16,000. MPG: 29 city, 40 highway.

Car 2: 2012 Toyota Prius. $23,000 MPG: 53 city, 46 highway. 2 years service.

Other information on request.

Question Five:

Sid's summer job is working at a roadside stand that sells ice cream. The manager, being the type of manager that manages by making others do all the work, asks Sid to order all the needed cones for the ice cream stand. Understanding the current job market and realizing that if the ice cream stand were to fold, Sid would have trouble finding other work at short notice, Sid agrees and starts to accrue information necessary to a proper cone purchase:

• Two types of cones are needed at the stand: standard cones and waffle cones.

• The roadside stand storage can hold, at most, 12 boxes of cones.

• There is $800 allotted for cones. Sid briefly considers stealing the money and leaving the manager high and dry, but that's just not really who Sid is, and besides, tips on the cones over the summer should be higher than $800.

• A box of standard cones is $30.

• A box of waffle cones is $80.

• What should Sid order? Are there other considerations that Sid should be thinking about?

Question Six: "Write" Stuff

(see sheet)