Mixture Problems This lesson must be completed with the mixture handout
Jan 03, 2016
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