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 = 12.50x or y = 12.5x
y = 5.5x + 1400
Choose a method: graph, substitution, elimination.
y = 5.5x + 1400
( 12.5x ) = 5.5x + 1400
12.5x = 5.5x + 1400
7x = 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:
Tank 2:
g = 10h + 50
g = 3h + 29
Solve the system
g = 10h + 50
solve for g:
(3h + 29) = 10h + 50
g = 10h + 50
Hours = -3
Gallons = 20
3h + 29 = 10h + 50
g = 10( -3 ) + 50
Answer?
-7h+ 29 = 50
-7h = 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