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Mixture Problems

Many real world problems involve combinations of two or more quantities that make up a new quantity. Such problems are called mixture problems. Mixture problems follow the same pattern as investment problems and money problems.

These problems often give us information needed to find another total by multiplying the number of items by the value of each item. Algebra word problem consists of data which are arranged to solve part by part and then to derive the solution for end results. Below is the generic form of the verbal model for mixture problems:

  Model for Mixture Problems

Let us see with the help of example how to construct and solve the mixture problems:
 
Example: Rosar wants to mix almond worth $\$$10 per pound with 21 pound of peanuts worth $\$$5 per pound. To obtain a nut mixture worth $\$$8 per pound, how many pound of almonds are needed? How many pounds of mixed nuts will be produced for the Rosar.

Solution:
In this problem, the rates are the unit prices of the nuts.

Let the amount of almonds = x

   Unit Price
 Amount  Value
Almonds
  10
 x  10 x
 Peanuts  5  21  5 $\times$ 21
 Mixed nuts  8  x + 21  8 (x + 21)

So we have

10x + 5 $\times$ 21 = 8 (x + 21)

10x + 105 = 8x + 168

Solve for x

10x - 8x = 168 - 105

2x = 63

x = 31.5

Thus, Rosar needs 31. 5 pounds of almonds. This will result in x + 21 = 31.5 + 21 = 52.5 pounds of mixed nuts.

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