Algebra Mixture Problems

Mixture problems are word problems where items or quantities of different values are mixed together.

We recommend using a table to organize your information for mixture problems. Using a table allows you to think of one number at a time instead of trying to handle the whole mixture problem at once.

Removing From The Solution

Example:

John has 20 ounces of a 20% of salt solution. How much water should he evaporate to make it a 25% solution?

Solution:

Step 1: Set up a table for water. The water is removed from the original.

	original	removed	result
concentration
amount

Step 2: Fill in the table with information given in the question.

John has 20 ounces of a 20% of salt solution. How much water should he evaporate to make it a 30% solution?

The original concentration of water is 100% – 20% = 80%
The resulted concentration of water is 100% – 30% = 70%
The water evaporated is 100% water, which is 1 in decimal.

Change all the percent to decimals.

Let x = amount of water evaporated. The result would be 20 – x.

	original	removed	result
concentration	0.8	1	0.7
amount	20	x	20 – x

Step 3: Multiply down each column.

	original	removed	result
concentration	0.8	1	0.7
amount	20	x	20 – x
multiply	0.8 × 20	1 × x	0.70(20 – x)

Step 4: Since the water is removed, we need to subtract

original – removed = result
0.8 × 20 – 1 × x = 0.70(20 – x)
16 – x = 14 – 0.7x

Isolate variable x
x – 0.7x ­= 16 – 14
0.3x = 2

Answer: He should evaporate 6.67 ounces of water.

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