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Mixture problems—problems that involve combining
two or more items—occur in many different settings. Example 5 discusses
mixing roasted nuts and raisins. The exercise set presents mixture problems from
other fields, such as chemistry.
MIXTURE PROBLEMS
EXAMPLE
5
Solve a Mixture Problem
A store sells a mixture of raisins and roasted nuts.
Raisins cost $3.50 per kilogram and nuts cost $4.75 per kilogram. How many
kilograms of each should be mixed to make 20 kilograms of this snack worth
$4.00 per kilogram?
RAISINS AND NUTS
Student Help
STUDY TIP
Because the number
of kilograms of the
mixture is 20 and the
number of kilograms of
raisins is x, the number
of kilograms of nuts is
20 x.
Solution
When you solve a mixture problem, it is helpful to make a chart.
Let x Number of kilograms of raisins.
Then 20 x Number of kilograms of nuts.
Use the information from the problem to complete the chart below. Then write
and solve an equation that relates the cost of the raisins, the cost of nuts, and
the cost of mixture.
Number of kg Price per kg Cost
Raisins
x
3.50
3.5x
Nuts
20 x
4.75
4.75(20 x)
Mixture
20
4.00
80
Cost of raisins Cost of nuts Cost of mixture
Write verbal model.
3.5x 4.75(20 x) 80
Write algebraic model.
350x 475(20 x) 8000
Multiply each side by
100 to clear equation
of decimals.
350x 9500 475x 8000
Use distributive property.
9500 125x 8000
Combine like terms.
125x 1500
Subtract 9500 from
each side.
x 12
Divide each side by 125.
Therefore, 20 x 8
ANSWER 䊳
12 kilograms of raisins and 8 kilograms of nuts are needed.
Solve a Mixture Problem
9. You make a mixture of dried apples costing $6.00 per kilogram and dried
apricots costing $8.00 per kilogram. How many kilograms of each do you
need to make 10 kilograms of a mixture worth $7.20 per kilogram? Make a
chart to help you solve the problem.
11.7
Rational Equations
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