SECTION 3-3Linear-Combination Situations

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

2B + 3C = 20

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

2B + 3C = 203 Combinations

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

2B + 3C = 203 Combinations

7 loaves of bread, 2 cakes

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

2B + 3C = 203 Combinations

7 loaves of bread, 2 cakes4 loaves of bread, 4 cakes

WARM-UPAt a bake sale, bread costs $2 a loaf and cakes coast $3 each. Suppose you want to buy some bread and cake and spend

exactly $20. How many different combinations of bread and cake can you buy?

B = Bread, C = Cake, A = Total Amount

2B + 3C = 203 Combinations

7 loaves of bread, 2 cakes4 loaves of bread, 4 cakes1 loaves of bread, 6 cakes

LINEAR COMBINATION

LINEAR COMBINATION

An expression of the form Ax + By, where A and B are constants

LINEAR COMBINATION

An expression of the form Ax + By, where A and B are constants

All variables are to the first degree

LINEAR COMBINATION

An expression of the form Ax + By, where A and B are constants

All variables are to the first degree

The variables are not multiplying or dividing each other

LINEAR COMBINATION

An expression of the form Ax + By, where A and B are constants

All variables are to the first degree

The variables are not multiplying or dividing each other

Gives the graph of a line (or line segment)

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

A = Adult tickets, K = Kid tickets, T = Total amount

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

A = Adult tickets, K = Kid tickets, T = Total amountT = 5A + 2K

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

A = Adult tickets, K = Kid tickets, T = Total amountT = 5A + 2K36 = 5A + 2K

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

A = Adult tickets, K = Kid tickets, T = Total amountT = 5A + 2K

b. Make a table and graph.36 = 5A + 2K

EXAMPLE 1Matt Mitarnowski sold $36 worth of tickets for the Big Guy

Club Picnic. Adult tickets cost $5 and kid tickets cost $2.

a. Write an equation

A = Adult tickets, K = Kid tickets, T = Total amountT = 5A + 2K

b. Make a table and graph.

K 18 13 8 3

A 0 2 4 6

36 = 5A + 2K

EXAMPLE 1

0

2

4

6

8

0 4.5 9.0 13.5 18.0

Kid

Tic

kets

Adult Tickets

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

A = Mixture A, B = Mixture B, T = Total

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

.05A + .15(50) = 12

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

.05A + .15(50) = 12.05A + 7.5 = 12

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

.05A + .15(50) = 12.05A + 7.5 = 12

.05A = 4.5

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

.05A + .15(50) = 12.05A + 7.5 = 12

.05A = 4.5A = 90 oz

EXAMPLE 2Mixtures A and B contain weed killer and water. Mixture A is

5% weed killer and mixture B is 15% weed killer.a. Write an equation

.05A + .15B = TA = Mixture A, B = Mixture B, T = Total

b. How many ounces of 5% solution must be added to 50 oz. of 15% solution to get 12 oz. of weed killer?

.05A + .15(50) = 12.05A + 7.5 = 12

.05A = 4.5A = 90 oz of Mixture A must be added

EXAMPLE 2c. Graph a situation where the final mixture gives 12 ounces

of weed killer in the final mix.

EXAMPLE 2c. Graph a situation where the final mixture gives 12 ounces

of weed killer in the final mix.A B0 8026 0

EXAMPLE 2c. Graph a situation where the final mixture gives 12 ounces

of weed killer in the final mix.A B0 8026 0

0

20

40

60

80

0 75 150 225 300

Mix

ture

B

Mixture A

EXAMPLE 2c. Graph a situation where the final mixture gives 12 ounces

of weed killer in the final mix.A B0 8026 0

0

20

40

60

80

0 75 150 225 300

Mix

ture

B

Mixture A

HOMEWORK

HOMEWORK

p. 155 #1 - 19

“Hold yourself responsible for a higher standard than anyone else expects of you. Never excuse yourself.”

-Henry Ward Beecher