objective: to be able to solve linear systems graphically pod graph the following piecewise function
DESCRIPTION
Problem: The chex snack company would like to market a new snack that will contain nuts and dried fruit. The cost of a lb of nuts is $1 and the cost of a lb of dried fruit is $2. The company would like to keep the cost of the bag at $4, and at the same time the amount of nuts in the mixture should be 2 times as many as the dried fruit for optimal taste. Question: How many lbs of dried fruits and how many lbs of nuts should be used in each bag?TRANSCRIPT
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Objective: To be able to solve linear systems graphicallyPOD Graph the following piecewise function
1 3, if 2 2
( ) 2, if 2 11, if 1
x x
f x x xx
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Try another one for practice
2 4, if 2 3
( ) 3, if 2 23 4, if 22
x x
f x x
x x
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Problem: The chex snack company would like to market a new snack that will contain nuts and dried fruit. The cost of a lb of nuts is $1 and the cost of a lb of dried fruit is $2. The company would like to keep the cost of the bag at $4, and at the same time the amount of nuts in the mixture should be 2 times as many as the dried fruit for optimal taste.
Question: How many lbs of dried fruits and how many lbs of nuts should be used in each bag?
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A problem like this involves a system(2 equations acting on the same variables)Let y represent the lbs of nuts in the mixtureLet x represent the lbs of dried fruit in the mixture
Write an equation that related the numbers of lbs of nuts and dried fruit that can be bagged for $4
Write an equation that related the numbers of lbs of nuts and dried fruit to represent the taste preference
1) The Cost
2) The Taste
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NUTS(y)
DRIED FRUIT(x)
HOW MANY LBS NUTS AND HOW MANY LBS FRUIT SHOULD BE USED IN THE MIX?
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Ex. 1 Solve the system Ex. 2 Try this one
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Ex. 3 Solve the system Ex. 4 Solve the system
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Types of situations in solving linear systemsEx. 5 Solve the system2x + 3y = 64x + 6y = 12
Ex. 6 Solve the system2x + y = 42x + y = 1
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Graphing Systems Results in The following Situations
Number of Solutions Number of Solutions Number of Solutions
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Ex. 7 Ex. 8
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Ex. 9 Solve the systemy = 3 + 4x20x - 5y = -15
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