Solving mixture problems follows the same method we like to do for all rate x time = Distance questions. We make a matrix for r x t = D on the top but to fill it in we'll make an analogy. What are our terms instead of r and t? Look by the numbers in the question. In the question below we have 36 and next to it is an amount of money, so one of the terms will be price. Another value is 300 and next to it is a weight, so the other term is number of pounds. Does it matter which comes first? Well, let me ask you: what's 3 x 4? And what's 4 x 3? When we multiply across our matrix to get the "D" or Total value, the order in which we do it doesn't matter. Let's look at our example.
Example:
Mr. Thomson wants to mix candy worth 36 cents a pound with candy worth 52 cents a pound to make 300 pounds of a mixture worth 40 cents a pound. How many pounds of the more expensive candy should he use?
Solution:
Let's set up our r x t = D matrix using our analogie values of pounds, price and total.
The value of the more expensive candy plus the value of the less expensive candy must be equal to the value of the mixture. Almost all mixture problems derive their equation from adding the final column (The "D" or "Distance" value) in the chart. In this case, we changed our Distance to read Total Value.
52x + 36(300 – x) = 12000
Notice that all values were computed in cents to avoid decimals. As long as you multiply all the values of an equation you can manipulate them however you want.
52x+10,800−36x =12,000 16x = 1200
x = 75
He should use 75 pounds of the more expensive candy.
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