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Warm Up Tuesday August 26

Warm Up Tuesday August 26. Daniel sells magazine subscriptions and earns $4 for every new subscriber he signs up. Daniel also earns a $38 weekly bonus regardless of how many magazine subscriptions he sells.

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Warm Up Tuesday August 26

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  1. Warm UpTuesday August 26 Daniel sells magazine subscriptions and earns $4 for every new subscriber he signs up. Daniel also earns a $38 weekly bonus regardless of how many magazine subscriptions he sells. If Daniel wants to earn at least $91 this week, what is the minimum number of subscriptions he needs to sell?

  2. Answer To solve this, let's set up an expression to show how much money Daniel will make. Amount earned this week =Subscriptions sold × Price per subscription + Weekly bonus Since Daniel wants to make at least$91 this week, we can turn this into an inequality. Amount earned this week ≥$91 Subscriptions sold × Price per subscription + Weekly bonus ≥$91 We are solving for the number of subscriptions sold, so let subscriptions sold be represented by the variable x. We can now plug in: x⋅$4+$38≥$91 x⋅$4≥$91−$38 x⋅$4≥$53 x≥534≈13.25 Since Daniel cannot sell parts of subscriptions, we round 13.25 up to 14. Daniel must sell at least 14 subscriptions this week.

  3. Time for our Pre-Test. Try all problems. You have 45 minutes. You may or may not know how to do them but give your best effort

  4. Partner time  Discuss this problem with a partner. A plane is about to take off from an airport. Using math terms that you have learned in the past, explain the process of the flight from beginning to end.

  5. THE ENTIRE FLIGHT IS LINEAR!!!

  6. Linear Equations So what do you know about linear equations?

  7. 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

  8. 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

  9. 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

  10. Formulas Slope formula Direct variation Slope-intercept form Point-slope form Standard form of an equation

  11. #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?

  12. 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

  13. Complete worksheets on linear equations

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