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Section 6.4 Applications of Linear System

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Break even point

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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 soldy = the # of dollars of expense or income Write a system of equations. Income: Expense: y = 12.50x or y = 12.5x y = 5.5x Choose a method: graph, substitution, elimination. y = 5.5x ( ) = 5.5x x 12.5x = 5.5x x = 1400 x = 200 Answer? 200 hats

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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: Tank 2: g = 10h + 50 g = 3h + 29 Solve the system g = 10h + 50 ( ) = 10h h h + 29 = 10h h+ 29 = 50 -7h = 21 h = -3 solve for g: g = 10h + 50 g = 10( ) g = g = 20 Hours = -3 Gallons = 20 Answer? 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. Never: it is impossible to have time be -3 hours.

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

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