A milk vendor has 2 cans of milk. The first contains 35% water and the rest milk. The second contains 65% water. How much milk should he mix from each of the container so as to get 64 liter of milk. Such that the ratio of water to milk is 3:7?
Question
A milk vendor has 2 cans of milk. The first contains 35% water and the rest milk. The second contains 65% water. How much milk should he mix from each of the container so as to get 64 liter of milk. Such that the ratio of water to milk is 3:7?
Solution
This problem can be solved using the method of Allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.
Step 1: Let's denote the amount of milk from the first can as x liters and from the second can as y liters.
Step 2: We know that the total amount of milk is 64 liters. So, we can write the equation as: x + y = 64.
Step 3: The first can contains 35% water, which means it contains 65% milk. The second can contains 65% water, which means it contains 35% milk.
Step 4: We also know that the ratio of water to milk in the final mixture is 3:7, which means the mixture contains 70% milk and 30% water.
Step 5: We can now write the second equation using the percentages of milk from each can and the total amount of milk: 0.65x + 0.35y = 0.7 * 64.
Step 6: Now we have a system of two equations: x + y = 64 and 0.65x + 0.35y = 44.8.
Step 7: Solve this system of equations to find the values of x and y.
By solving these equations, we can find out how much milk should be mixed from each of the containers.
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