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
x=2/0.3

Answer: He should evaporate 6.67 ounces of water.

 

 

Video

Mixture Problems
Some word problems using systems of equations involve mixing two quantities with different prices. To solve mixture problems, knowledge of solving systems of equations. is necessary. Most often, these problems will have two variables, but more advanced problems have systems of equations with three variables. Other types of word problems using systems of equations include rate word problems and work word problems.

 

 

 

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