Objective: To SolveMixture Problems

Mixture problems involve combining two mixtures to make one final mixture.

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We are going to use buckets to help solve these problems.

Buckets

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

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STEP #1: Draw buckets

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

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Step #1: Draw the buckets

STEP #2: Label the buckets

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

Step #1: Draw the buckets

Step #2: Label the buckets

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STEP #3: Price or Percent goes on top

100% 10% 40%

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

Step #1: Draw the bucketsStep #2: Label the buckets

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Step #3: Price or Percent goes on top

100% 10% 40%

STEP #4: Change Percents to decimals

= 1 = 0.1 = 0.4

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

Step #1: Draw the bucketsStep #2: Label the buckets

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Step #3: Price or Percent goes on top

100% 10% 40%

Step #4: Change Percents to decimals

= 1 = 0.1 = 0.4

STEP #5: Weight goes on the bottom

x 5 x + 5

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

Step #1: Draw the bucketsStep #2: Label the buckets

++ ==

Step #3: Price or Percent goes on top

100% 10% 40%

Step #4: Change Percents to decimals

= 1 = 0.1 = 0.4

Step #5: Weight goes on the bottom

x 5 x + 5

STEP #6: Set up and Solve

1. An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

++ ==100% 10% 40%= 1 = 0.1 = 0.4

x 5 x + 5

STEP #6: Set up and Solve

1x + 0.1(5) = 0.4(x+5)1.0x + 0.5 = 0.4x + 2

-0.4x -0.4x0.6x + 0.5 = 2.0

-0.5 -0.50.6x = 1.50.6 0.6x = 2.5

2.5 quarts of pureorange juice would have to be added to

the 5 quarts of the drink.

2. How much water would you have to add to 3 liters of lake water that is 30 percent salt to get a solution

that is only 12 percent salt? Step #1: Draw buckets

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Step #2: Label the bucketsStep #3: Percent or price goes on topStep #4: Change percents to decimalsStep #5: Amount goes on bottomStep #6: Set up and solve

0% 30% 12%= 0 = 0.3 = 0.12

x 3 x +3

++ ==0% 30% 12%= 0 = 0.3 = 0.12

x 3 x +3

#2

0(x) + 0.3(3) = 0.12(x+3)0 + 0.9 = 0.12x + 0.36

0.9 = 0.12x + 0.36-0.36 -0.36

0.54 = 0.12x + 00.54 = 0.12x0.12 0.12

x = 4.5

4.5 liters of water shouldbe added to the lake water

3. Sterling Silver is 92.5% pure silver. How many grams of pure silver and sterling silver must be mixed

to obtain 100g of a 94% Silver alloy? Step #1: Draw buckets

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Step #2: Label the bucketsStep #3: Percent or price goes on topStep #4: Change percents to decimalsStep #5: Amount goes on bottomStep #6: Set up and solve

92.5% 100% 94%= 0.925 = 1 = 0.94

x 100 - x 100

#3

++ ==92.5% 100% 94%= 0.925 = 1 = 0.94

x 100 - x 100

0.925x + 1 (100-x) = 0.94(100)

0.925x + 100 – 1x = 94

-0.075x + 100 = 94 -100 -100

-0.075x = -6-0.075 -0.075

x = 80

100 - x100 – 80 = 20

80 grams of the sterling silverand 20 grams

of the pure silverare needed.

4. A mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture which is 15% boric acid in order to obtain a solution which is 12% boric acid.

How much of the 6% solution must be used? Step #1: Draw buckets

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Step #2: Label the bucketsStep #3: Percent or price goes on topStep #4: Change percents to decimalsStep #5: Amount goes on bottomStep #6: Set up and solve

6% 15% 12%= 0.06 = 0.15 = 0.12

x 2 x + 2

++ ==6% 15% 12%= 0.06 = 0.15 = 0.12

x 2 x + 2

#4

0.06x + 0.15(2) = 0.12(x+2)

0.06x + 0.3 = 0.12x + 0.24-0.06x -0.06x

0.3 = 0.06x + 0.24-0.24 -0.24

0.06 = 0.06x0.06 0.06

1 = x

1 quart of the 6%boric acid mixtureshould be added.

5. ClearShine window cleaner is 12% alcohol and Sunstream cleaner is 30% alcohol. How much of each

should be used to make 90 oz. (ounces) of a cleaner that is 20% alcohol?

Step #1: Draw buckets

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Step #2: Label the bucketsStep #3: Percent or price goes on topStep #4: Change percents to decimalsStep #5: Amount goes on bottomStep #6: Set up and solve

12% 30% 20%= 0.12 = 0.3 = 0.20

x 90-x 90

++ == 12% 30% 20% = 0.12 = 0.3 = 0.20

x 90-x 90

#5

0.12x + 0.3(90-x) = 0.20(90)

0.12x + 27 - 0.3x = 18

-0.18x + 27 = 18-27 -27

-0.18x = -9-0.18 -0.18

x = 50

50 ounces of Clearshinewindow cleaner and 40ounces of Sunstream

window cleaner.