Mrs. Napholtz's Math Site
Mixture Problems
An owner of a gourmet food store has two varieties of herbal tea, one that costs $4.00 per kilogram and another that costs $5.00 per kilogram. How many kilograms of each type are needed to make 20 kg of a blend worth $4.60 per kilogram?
Amount | Unit Cost | Total Cost | |
Cheaper | n | 4 | 4n |
More Expensive | 20 - n | 5 | 100 - 5n |
MIXTURE | 20 | 4.60 | 92 |
Note: The total costs of the two types of tea combined must equal the final cost of the mixture!
4n + 100 - 5n = 92
-n + 100 = 92
-n = -8
n = 8
Answer: 8 kg of cheaper, 12 kg of more expensive
How many liters of pure acid must be added to 6 L of a 75% acid solution to make an 85% solution?
Amount | % Acid | Total Acid | |
Acid Solution | 6 | 0.75 | 4.5 |
Pure Acid | n | 1.00 | n |
RESULT | 6 + n | 0.85 | 5.1 + 0.85n |
Note: The total amount of acid in the original solution and in the pure acid combined must equal the total amount of acid in the result!
4.5 + n = 5.1 + 0.85n
0.15n = 0.6
n = 4
Answer: 4 L of pure acid must be added.
Joanne makes a mixture of dried fruits by mixing dried apples costing $6.00/kg with dried apricots costing $8.00/kg. How many kg of each are needed to make 20 kg of a mixture worth $7.20/kg?
Amount | Unit Cost | Total Cost | |
Dried Apples | n | 6 | 6n |
Dried Apricots | 20 - n | 8 | 160 - 8n |
MIXTURE | 20 | 7.20 | 144 |
The total costs of the apples and dried apricots combined must equal the final cost of the mixture!
6n + 160 - 8n = 144
-2n + 160 = 144
-2n = -16
n = 8
Answer: 8 kg of dried apples, 12 kg of dried apricots.
A grocer makes a natural breakfast cereal by mixing oat cereal costing $2 per kg with dried fruits costing $9 per kg. How many kg of each are needed to make 60 kg of cereal costing $3.75 per kg?
Amount | Unit Cost | Total Cost | |
Oat Cereal | n | 2 | 2n |
Dried Fruits | 60 - n | 9 | 540 - 9n |
MIXTURE | 60 | 3.75 | 225 |
The total costs of the oat cereal and dried fruits combined must equal the final cost of the mixture!
2n + 540 - 9n = 225
-7n + 540 = 225
-7n = -315
n = 45
Answer: 45 kg of oat cereal, 15 kg of dried fruits.
How many liters of water must be added to 20 L of a 24% acid solution to make a solution that is 8% acid?
Amount | % Acid | Total Acid | |
Acid Solution | 20 | 0.24 | 4.8 |
Water | n | 0 | 0 |
RESULT | 20 + n | 0.08 | 1.6 + 0.08n |
Note: The total amount of acid in the original solution and in the water combined must equal the total amount of acid in the result!
Note: There is NO acid in the water!
4.8 + 0 = 1.6 + 0.08n
3.2 = 0.08n
n = 40
Answer: 40 L of water must be added.
How many kg of water must be evaporated from 12 kg of a 5% salt solution to produce a solution that is 30% salt?
Amount | % Salt | Total Salt | |
Salt Solution | 12 | 0.05 | 0.6 |
Water | n | 0 | 0 |
RESULT | 12 - n | 0.30 | 3.6 - 0.30n |
Note: The total amount of salt in the original solution and in the water combined must equal the total amount of salt in the result!
Note: There is NO salt in the water!
Note: Due to evaporation, we subtract the amount of water from the original amount of solution!
0.6 - 0 = 3.6 - 0.30n
-3.0 = -0.30n
n = 10
Answer: 10 kg of water must be evaporated.