Mixture Word Problems - Different Costs or Concentrations

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.

Mixing Quantities Of Different Costs or Different Concentrations

Example:

How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound?

Solution:

Step 1: Set up a table for different types of chocolate.

	original	added	result
cost
amount

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

How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound?

Let x = amount of chocolate added.

	original	added	result
cost	0.9	1.2	1
amount	10	x	x + 10

Step 3: Multiply down each column.

	original	added	result
cost	0.9	1.2	1
amount	10	x	x + 10
multiply	0.9 × 10	1.2 × x	1 × (x + 10)

Step 4: original + added = result

0.9 × 10 + 1.2 × x = 1 × (x + 10)
9 + 1.2x = x + 10

Isolate variable x
1.2x – x = 10 - 9
0.2x = 1

Answer: 5 pounds of the $1.20 cents chocolate needs to be added.

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