Solving 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.

Replacing The Solution

Example:

A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70% solution?

Solution:

Step 1: Set up a table for alcohol. The alcohol is replaced i.e. removed and added.

	original	removed	added	result
concentration
amount

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

A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70% solution?

Change all the percent to decimals.

Let x = amount of alcohol solution replaced.

	original	removed	added	result
concentration	0.15	0.15	0.8	0.7
amount	10	x	x	10

Step 3: Multiply down each column.

	original	removed	added	result
concentration	0.15	0.15	0.8	0.7
amount	10	x	x	10
multiply	0.15 × 10	0.15 × x	0.8 × x	0.7 × 10

Step 4: Since the alcohol solution is replaced, we need to subtract and add.

original – removed + added = result
0.15 × 10 – 0.15 × x + 0.8 × x = 0.7 × 10
1.5 – 0.15x + 0.8x = 7

Isolate variable x
0.8x – 0.15x = 7 – 1.5
0.65x = 5.5

Answer: 8.46 gallons of alcohol solution needs to be replaced.

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