Mixture Word 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.

Adding To The Solution

Mixture Problems: Example:

John has 20 ounces of a 20% of salt solution, How much salt should he add to make it a 25% solution?

Solution:

Step 1: Set up a table for salt.

	original	added	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 salt should he add to make it a 25% solution?

The salt added is 100% salt, which is 1 in decimal.
Change all the percent to decimals

Let x = amount of salt added. The result would be 20 + x.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x

Step 3: Multiply down each column.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x
multiply	0.2 × 20	1 × x	0.25(20 + x)

Step 4: original + added = result

0.2 × 20 + 1 × x = 0.25(20 + x)
4 + x = 5 + 0.25x

Isolate variable x
x – 0.25x = 5 – 4
0.75x = 1

Answer: He should add ounces of salt.

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