Writing systems of equations

1/21 and 1/22

Please have your binders out and place the notes for today in the binders.

Binders

Equations can be used to ______________ situations involving ________________.

If we can create a __________________________, we can solve for unknown quantities.

To solve for two unknown quantities we need________________ equations.

Systems of Equations

Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of  water can each pitcher hold?

Volumes

Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of  water can each pitcher hold?

Volumes Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Basketball

In a basketball game, Will scored 26 points, consisting only of three-point shots and two-point shots. He made a total of 11 shots. How many shots of each type did he make?

Basketball Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

Tests Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Your Turn

Tickets to a concert cost either $12 or $15. A total of 300 tickets are sold, and the total receipts were $4140. How many of each kind of ticket were sold?

Tickets Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

How do you become rich?

What is stock?

Why do you want stock?

Why is stock dangerous?

Stock

An investor buys a total of 360 shares of two stocks. The price of one stock is $35 per share, while the price of the other stock is $45 per share. The investor spends a total of $15000. How many shares of each stock did the investor buy?

Tickets Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Break

But let’s say we have the following situation.  You’re going to the mall with your friends and you have $200 to spend from your recent birthday money. You discover a store that has all jeans for $25 and all dresses for $50.  You really, really want to take home 6 items of clothing because you “need” that many new things.

Writing and Graphing Systems Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Graph these equations

Find the value of two numbers if their sum is 12 and their difference is 4.

Writing and Graphing Systems Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Graph these equations

Mini-Project Assignment

Create a mini-poster on which you write and graph a system of equations for two word problems.

You must:Label unknownsIdentify givensWrite equations that relate unknowns and givensGraph the equationsIdentify the solution from the graph

You are doing what we just did for the last two problems.

Requirements

Use the paper provided.Use color.Use a ruler to make straight graphs.

Grade on:Correctness: 70%Neatness (lines straight, writing even): 20%Organization (boxes to separate parts): 10$

Example:Find the value of two

numbers if their sum is 12 and their difference is 4.

Label unknowns:

Identify givens:

Write equations that relate unknowns and givens:

Solution:

The difference of two numbers is 3. Their sum is 13. Find the numbers.

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation. Then he solved the system by graphing. What is the solution?

The Two Problems: One Front, One Back

◦ Finish your poster

Homework