Section 6 4 Applications of Linear System Break

Section 6. 4 Applications of Linear System

Break even point

A fashion designer makes and sells hats. The material for each hat costs $5. 50. The hats sell for $12. 50 each. The designer spends $1400 on advertising. How many hats must the designer sell to break even? Define Variables: x = number of hats sold y = the # of dollars of expense or income Write a system of equations. Income: Expense: y = 12. 50 x or y = 12. 5 x y = 5. 5 x + 1400 Choose a method: graph, substitution, elimination. y = 5. 5 x + 1400 ( 12. 5 x ) = 5. 5 x + 1400 12. 5 x = 5. 5 x + 1400 7 x = 1400 x = 200 Answer? 200 hats

The local zoo is filling two water tanks for the elephant exhibit. One water tank contains 50 gal of water and is filled at a constant rate of 10 gal/h. The second water tank contains 29 gal of water and is filled at a constant rate of 3 gal/h. When will the two tanks have the same amount of water? Explain. Write a system of equations. Let h = the number of hours the tanks are filling. Let g = the number of gallons in the tank. Tank 1: g = 10 h + 50 Tank 2: g = 3 h + 29 Solve the system g = 10 h + 50 solve for g: (3 h + 29) = 10 h + 50 g = 10 h + 50 Hours = -3 Gallons = 20 3 h + 29 = 10 h + 50 g = 10( -3 ) + 50 Answer? -7 h+ 29 = 50 -7 h = 21 g = -30 + 50 g = 20 h = -3 Never: it is impossible to have time be -3 hours.

Assignment: Pg 390: 7 -10, 13 -16, 19 -21