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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.

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

resultcost

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

resultcost

0.9

1.2

1

amount

10

x

x+ 10

Step 3: Multiply down each column.

original

added

resultcost

0.9

1.2

1

amount

10

x

x+ 10multiply

0.9 × 10

1.2 ×

x1 × (

x+ 10)

Step 4: original + added = result

0.9 × 10 + 1.2 ×

x= 1 × (x+ 10)

9 + 1.2x=x+ 10Isolate variable

x1.2

x–x= 10 - 9

0.2x= 1

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

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.

Mixing Quantities Of Different Costs

Example: At the Grind House, Honduran coffee sells for $8.00 per pound and Costa Rican coffee sells for $11.50 per pound. If one pound of the Central American Blend coffee contains 0.4lb Costa Rican coffee and 0.6lb Honduran coffee, how much should one pound sell for?

Example: How many liters of a 10% salt solution should be added to 80 liters of a 35% salt solution to obtain a mixture that is a 30% salt solution?

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