∴ Mixture Problems General Questions
1. In a mixture problem, there are usually three items — the original mixture, the element which is added or removed, and the final mixture.
To solve mixture problems:
(a) Determine which element of the mixture will not change.
(b) Ascertain the exact amount of that element.
(c) Establish a relation between the amount of this stable element and the final mixture.
(d) Solve to find the final mixture.
(e) Subtract the original mixture from the final mixture to find the amount to be added.
Example:In a 20 gallon mixture of milk and water, there is 5% water. How much water must be added to make it 10% of the final mixture?
Solution: In this problem, water is to be added. Therefore, the element which will not change is the milk.
Since there is 5% water, the amount of milk must be 95% of the original mixture.
95% of 20 gallons = .95 x 20 = 19 gallons of milk
In the final mixture, there will be 10% water. Therefore, the milk will be 90% of the final mixture.
19 gallons of milk = 90% of the final mixture.
19 = 90/100 of the final mixture
19 = 9/10 of the final mixture
Therefore, final mixture = 19/9/10 = 19 * 10/9 = 190/9
= 21 1/9 gallons
The amount to be added = 21 1/9 gallons
The amount to be added = 21 1/9 - 20 = 1 1/9 gallon
3. When a mixture is made of two different grades of an article, to find the amount of each:
(a) Multiply the total mixture by the value of the lower grade.
(b) Multiply the total mixture by the value of the lower grade.
(c) Subtract this product from the total value.
(d) Divide by the difference in the two grades to find the amount of the higher grade in the mixture.
(e) To find the amount of the lower grade in the mixture, simply subtract from the total mixture.
Example: How many pounds of Rs. 25 a lb. coffee have to be mixed with Rs. 40 a lb. coffee to make a mixture of 60 pounds worth Rs. 35 a pound?
Solution: (i) 60 x Rs. 35 = Rs. 2100 total value
(ii) 60 * 25 = Rs. 1500
Rs. 2100 - Rs. 1500 = Rs. 600
The difference in the two grades = 40-25 = 15
Rs. 600/15 = 40
60 - 10 = 20
Answer: 40 pounds of the Rs. 40 a lb. coffee
20 pounds of the Rs. 25 a lb. coffee