Mixture Problems

This lesson must be completed with the mixture handout

Partner Brainstorm

If you mix 50 apples and 25 peaches in a basket, what part of the basket mixture is apples?

What percent of the basket mixture is peaches?

50 apples out of a total of 75 fruits

25 apples out of a total of 75 fruits

25 = x % = 33%

75 100

Solve problems that use“is over of equals percent over 100”

If a mixture of 10 items is 60% nails, how many nails are in the mixture?

If a mixture of 60 items is 40% pencils, how many pencils are in the mixture?

Handout Problem 1Mixing Chemicals

Suppose you work in a lab. You need a 50% acid solution for a lab test, but your supplier only ships a 40% solution and a 70% solution. Rather than pay extra fees you decide to mix the acids yourself. You are using 50 liters of the 40% solution. How many liters of a 70% acid solution do you need to get 50% acid?

STEP 1: Set up table

How many liters of a 70% acid solution must be added to 50 liters of a 40% acid solution

to produce a 50% acid solution?STEP 1: Set up and fill in table with information

then multiply across the table

Solution xAmount

% Acid = Total Acid

70% Solution

40% Solution

TotalMixture

X 0.70 0.70x

50 0.40 (50)(0.40)=20

50+x 0.50 (50+x)(0.50)

STEP 2: Add up last column and write an equation

Solution xAmount

% Acid = Total Acid

70% Solution

X 0.70 0.70x

40% Solution

50 0.40 (50)(0.40) =20

TotalMixture 50 + x 0.50 (50+x)(0.50)

0.7x + 20 = 0.5(50+x)

Solve for x and compare answers

STEP 1:Set up and fill table

Solution xAmount

% Salt = Total Salt

Water

15% Solution

10%Mixture

X 0 0x = 0

50 0.15 (50)(0.15)=7.5

50+x 0.10 (50+x)(0.10)

Handout Problem 2Mixing Water

How many ounces of pure water must be added to 50 ounces of a 15% salt solution to make a salt solution that

is 10% salt?

Solution xAmount

% Salt = Total Salt

Water

15% Solution

10%Mixture

X 0 0x = 0

50 0.15 (50)(0.15)=7.5

50+x 0.10 (50+x)(0.10)

STEP 2: Add up last column and write an equation

0 + 7.5 = 0.1(50+x)

Solve for x and compare answers

STEP 1:Set up and fill table

Coffee xAmount

$per lb = Total $ for coffee

Pricey

Cheapo

Mixture

8 $9.20 (8)($9.20)

=$73.60

12 $5.50 (12)($5.50)

=$66

8+12=20 ? Add em=139.60

Handout Problem 3Coffee Mixture

Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and

12 pounds of coffee that costs $5.50 per pound

Coffee xAmount

$per lb = Total $ for coffee

Pricey

Cheapo

Mixture

8 $9.20 (8)($9.20)

=$73.60

12 $5.50 (12)($5.50)

=$66

8+12=20 ? Add em=139.60

From the last row, you see that you have 20 pounds for $139.60 or $139.60/(20 pounds). Simplify

STEP 1:Set up and fill table

Veggie xAmount

$per lb = Total $ for veggies

Lima Beans

Corn

Mixture

x $0.90 (x)($0.90)

16 $0.50 (16)($0.50)

=$8

16+x $0.65 (16+x)($0.65)

Handout Problem 4Veggies

How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 lbs of corn that costs $0.50

per pound to make a mixture of vegetables that costs $0.65 per pound?

Veggie xAmount

$per lb = Total $ for veggies

Lima Beans

Corn

Mixture

x $0.90 (x)($0.90)

16 $0.50 (16)($0.50)

=$8

16+x $0.65 (16+x)($0.65)

$0.90x + $8 = (16+x)($0.65)Solve for x

STEP 2: Add up last column and write an equation

STEP 1:Set up and fill table

Punch xAmount

%juice = Total liters juice

35% Fruit Juice

Other punch

Mixture

200 0.35 (200)(0.35)

=70

300 x (300)(x)

200+300=500 0.20 (500)(0.20)

=100

Handout Problem 5Fruit Drinks

Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters (L) of another punch. The

resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch

Punch xAmount

%juice = Total liters juice

35% Fruit Juice

Other punch

Mixture

200 0.35 (200)(0.35)

=70

300 x (300)(x)

200+300=500 0.20 (500)(0.20)

=100

70 +300x = 100Solve for x, and then convert to a percent

STEP 2: Add up last column and write an equation

STEP 1:Set up and fill table

Gram xAmount

%sugar =

Total grams sugar

Cereal

Sugar

Mixture

40 0.30 (40)(0.30)=12

10 1.00 (10)(1)=10

(100%sugar)

50 ? 10+12=22

Handout Problem 6Breakfast Cereal

Ten grams of sugar are added to a 40 gram serving of a breakfast cereal that is 30% sugar. What is the percent

concentration of sugar in the resulting mixture?

Gram xAmount

%sugar =

Total grams sugar

Cereal

Sugar

Mixture

40 0.30 (40)(0.30)=12

10 1.00 (10)(1)=10

(100%sugar)

50 ? 10+12=22

22 grams of sugar in the 50 gram bowl so 22/50

simplify and then convert to a percentage