SOLUTION: The manager of a store selling tea plans to mix a more expensive tea that costs $6 per pound with a less expensive tea that costs $3 per pound to create a 90​-pound blend tha

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Question 1109894: The manager of a store selling tea plans to mix a more expensive tea that costs $6 per pound with a less expensive tea that costs $3 per pound to create a 90​-pound blend that will sell for $3.90 per pound. How many pounds of each type of tea are​ required?
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Answer by josgarithmetic(39625) About Me  (Show Source):
Answer by greenestamps(13203) About Me  (Show Source):
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The fastest way to solve "mixture" problems like this, where two ingredients are being mixed, is the method of alligation. Do a search of the internet if you want to learn more about that method.

The method is based on the fact that the ratio in which the two ingredients are mixed exactly determines where the cost of the mixture lies between the costs of the individual ingredients.

Here is the diagram for solving your problem using the method of alligation:

matrix%283%2C3%2C6.00%2C%22%22%2C.90%2C%22%22%2C3.90%2C%22%22%2C3.00%2C%22%22%2C2.10%29

The numbers in the first column are the per-pound prices of the two kinds of tea; the number in the middle column is the per-pound cost of the mixture.

The numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second columns: 6.00-3.90 = 2.10 and 3.90-3.00 = .90.

When the calculations are done this way, the numbers in the third column show the ratio in which the two kinds of tea must be mixed.

In this problem, that ratio is .90:2.10 = 9:21 = 3:7. So the mixture must contain 3 parts of the expensive tea to 7 parts of the cheaper tea. You can also think of that as meaning the mixture must be 3/10 the expensive tea and 7/10 the cheaper tea.

Whichever way you think of it, 90 pounds of the mixture means 27 pounds of the expensive tea and 63 pounds of the cheaper tea.