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Warm Up Wednesday August 27

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Warm Up

Wednesday August 27

For every level Christopher completes in his favorite game, he earns 940 points. Christopher already has 430 points in the game and wants to end up with at least 2410 points before he goes to bed.

What is the minimum number of complete levels that Christopher needs to complete to reach his goal?

Answer

To solve this, let's set up an expression to show how many points Christopher will have after each level.

Number of points =Levels completed × Points per level + Starting points

Since Christopher wants to have at least2410 points before going to bed, we can set up an inequality.

Number of points ≥2410

Levels completed × Points per level + Starting points ≥2410

We are solving for the number of levels to be completed, so let the number of levels be represented by the variable x .

We can now plug in:

x⋅940+430≥2410

x⋅940≥2410−430

x⋅940≥1980

x≥1980940≈2.11

Since Christopher won't get points unless he completes the entire level, we round 2.11 up to 3 .

Christopher must complete at least 3 levels.

Linear Equations

So what do you know about linear equations?

Websites

http://www.mathsisfun.com/algebra/linear-equations.html

http://www.mathsisfun.com/algebra/line-equation-2points.html

http://www.mathsisfun.com/algebra/line-parallel-perpendicular.html

Why is this important?

#1 A machine salesperson earns a base salary of $40,000 plus a commission of $300 for every machine he sells. Write an equation that shows the total amount of income the sales person earns, if he sells x machines in a year.

#2 At a school play, children’s tickets cost $3 each and adult

tickets cost $7 each. The total amount of money earned from ticket

sales equals $210. Write a linear model that relates the number of

children’s tickets sold to the number of adult tickets sold

Answer#1:

The linear model representing the salesperson’s total income is y = $300x+ $40,000

Answer#2

Let x= the number of children’s tickets sold

And y= the number of adult tickets sold

The amount of money earned from children’s tickets is 3x.

The amount of money earned from adult tickets is 7y.

The total amount of money earned

from ticket sales is 3x+ 7y, which is equal to $210.

Answer: 3x+ 7y= 210

Formulas

Slope formula

Direct variation

Slope-intercept form

Point-slope form

Standard form of an equation

#3 Use the answer to #1 to answer (a) What would be the

salesperson’s income if he sold 150 machines? (b) How many

machines would the salesperson need to sell to earn a $100,000

income?

#4 In the ticket sales problem, how many children’s

tickets were sold if 24 adult tickets were sold?

Answer#3

(a)If the salesperson were to sell 150 machines, let x= 150 in the linear model; 300(150) + 40,000= 85,000.

Answer: His income would be $85,000.

(b) To find the number of machines he needs to sell to earn a $100,000 income, let y= 100,000 and solve forx:

y= 300x+ 40,000 Write the linear model.

100,000 = 300x+ 40,000 Substitute y= 100,000.

60,000 = 300x Subtract.

x= 200 Divide.

Answer: To earn a $100,000 income the salesperson would need to

sell 200 machines.

Answer#4 If 24 adult tickets were sold,y= 24. Substitute

y= 24 into the linear model for #2:

3x+ 7y= 210 Write the linear model.

3x+ 7(24) = 210 Substitute y= 24.

3x+ 168 = 210 Simplify.

3x= 42 Subtract.

x= 14 Divide.

Answer: 14 children’s tickets were sold

Try some of the worksheet questions

Lets check and see if we are all on the same page.

When do we ever use linear equations in real life?

- Temperature Conversion http://www.mathscore.com/math/practice/Temperature%20Conversion/
- Exchange Rates http://www.x-rates.com/table/?from=USD&amount=1.00
- Cell Phones
- http://www.verizonwireless.com/wcms/consumer/shop/prepaid.html
- Travel http://www.budget.com/budgetWeb/html/en/deals/wendie.html?&ICID=homepage_billboard&IID=wendie_august2013
- http://autos.aol.com/cars-Ford-Focus-2013/specs/mpg/

Here is a useful fact:

BMR stands for Basal Metabolic Rate. It is the number of calories you burn when you are being completely still.

We are going to do a little project to calculate what your personal BMR is and try to figure out if there is a linear relationship or not.

Homework

Finish selected problems from the linear equations worksheet AND

Complete and answer all the questions for the BMR Project (you don’t have to do scatter plots)