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