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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. - PowerPoint PPT Presentation
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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