University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2013
Views:

440

Pages:

4
Author:

otkucanoph8

Name: AW] = Notes # 6 - Standard Form Word Problems Class: Date: Equations With Two or More Variables You have done a lot of work with relationships involving two related variables. However, many real-world relationships involve three or more variables. For example, consider this situation: The eighth-graders are selling T-shirts and hats to raise money for their end-of-year party. They earn a profit of $5 per shirt and $10 per hats. This situation involves three variables: the number of T-shirts sold, the number of hats sold, and the profit. The profit for the fundraiser depends on the number of hats and the number of T-shirts sold. 1. What equation shows how the profit, p, is related to the number of shirts sold, s, and the number of hats, h, sold? P= 458 + 10h 2. 3. Find the profit if the students sell: a) 30 shirts and 50 hats 5(30) + 10(50)) 150 + 500 $650 b) 15 shirts and 10 hats 5(15) + 10(10) 75+100 $175 What ideas do you have for finding solutions to the equation? The equation relating p. s, and h represents every possible combination of T-shirts, hats, and profit values for the fundraiser. Suppose the class sets a profit goal of P = $600. Finding combinations of T-shirt and hat sales that meet this goal requires solving an equation with only" two variables, s and h. Solving Equations With Two Variables 4а) Write an equation that relates the number of t-shirts and hats sold to a $600 profit. 600 = 455+ $10h b) Find three pairs of solutions to your equation above; then graph the solutions below. (0,60) (20,50 ) (120, 0) (40, 40) T-Shirt and Cap Fund Raiser Profit 100 80 60k Number of Caps Sold 20 20 40 60 80 Number of T-Shirts Sold 100 c) Why does the graph only occur in the first quadrant? Explain. Can't have regatue hat/shirts. d) What do the coordinate pairs mean? Hint: in context to the word problem. # of sh.+-13 s01d #of he sadl Example 5: Students in Eric's gym class must cover a distance of 1,600 meters by running or walking. Most students run part of the way and walk part of the way. Eric can run at an average speed of 200 meters per minute and walk at an average speed of 80 meters per minute. a. If Eric runs for x minutes and walks for y minutes, write an cquation for the total distance that Eric will cover. 200x + 80y = 1000 B. Suppose Eric runs for 4 minutes and walks for 8 minutes, will be reach the finish 200(4) +80(8) ? 1600 800 + 640? 1600 1440 $ 1600 c. Find three pairs of solutions to your equation in part a. So No he want reach. (0,20) (4,10) (8,0) ete.