Lesson 2-9
Real-World Example 1
Mixture Problem
FRUIT A company sells a dried fruit mixture for $5 per pound. To make the mixture, banana chips that cost
$2.49 per pound are blended with dried strawberries that cost $7.95 per pound. How many pounds of dried
strawberries should be added to 3 pounds of banana chips to make the dried fruit mixture?
Step 1
Let w be the weight of the dried strawberries. Make a table to organize the information.
Number of
Units (lb)
3
w
3+w
Banana Chips
Dried Strawberries
Fruit Mixture
Price per Unit
($)
2.49
7.95
5
Total price
(price)(units)
2.49(3)
7.95w
5(3 + w)
Write an equation using the information in the table.
Price of
banana chips
Step 2
plus
price of
dried strawberries
2.49(3)
+
Solve the equation.
price of
fruit mixture.
equals
7.95w
=
5(3 + w)
2.49(3) + 7.95w = 5(3 + w)
7.47 + 7.95w = 15 + 5w
7.47 + 7.95w – 5w = 15 + 5w – 5w
7.47 + 2.95w = 15
7.47 + 2.95w – 7.47 = 15 – 7.47
2.95w = 7.53
w  2.6
Original equation
Distributive Property
Subtract 5w from each side.
Simplify.
Subtract 7.47 from each side.
Simplify.
Divide each side by 2.95.
To make the fruit mixture, about 2.6 pounds of dried strawberries should be added to the banana chips.
Real-World Example 2
Percent Mixture Problem
MILK Kayla wants to obtain a milk mixture that is 2% butterfat. How much 4% butterfat milk should she
mix with 8 cups of 1% butterfat milk to obtain the 2% butterfat milk?
Step 1
Let x = the amount of the 4% butterfat milk to be added. Make a table.
1% Butterfat Milk
4% Butterfat Milk
2% Butterfat Milk
Amount of Milk
(cups)
8
x
8+x
Amount of
Butterfat
0.01(8)
0.04x
0.02(8 + x)
Write an equation using the information in the table.
Amount of
Butterfat in 1%
Step 2
plus
Amount of
Butterfat in 4%
0.01(8)
+
0.04x
Solve the equation.
0.01(8) + 0.04x = 0.02(8 + x)
0.08 + 0.04x = 0.16 + 0.02x
0.08 + 0.04x – 0.02x = 0.16 + 0.02x – 0.02x
0.08 + 0.02x = 0.16
0.08 + 0.02x – 0.08 = 0.16 – 0.08
0.02x = 0.08
0.02 x 0.08
=
0.02
0.02
equals
Amount of
Butterfat in 2%
=
0.02(8 + x)
Original equation
Simplify.
Subtract 0.02x from each side.
Simplify.
Subtract 0.08 from each side.
Simplify.
Divide each side by 0.02.
x=4
Simplify.
Kayla should add 4 cups of 4% butterfat milk to 8 cups of 1% butterfat milk to obtain the 2% butterfat milk.
Real-World Example 3
Speed of One Vehicle
1
COMMUTE Jean drove to work in hour and drove home in 1 hour. If it is 40 miles from her
2
house to her work, what is Jean’s average speed for the round trip?
d
To find the average speed, rewrite d = rt as r = t .
Going to Work
Returning Home
d
d
r= t
r= t
40 mi
40 mi
= 0.5 h or 80 miles per hour
= 1 h or 40 miles per hour
Round Trip
80(0.5) + 40(1)
M=
0.5 + 1
80
= 1.5 or about 53.33
Definition of weighted average
Simplify.
Jean’s average speed was 53.33 miles per hour.
Real-World Example 4
Speeds of Two Vehicles
CYCLING Eli and Beth are 15.5 miles apart. Eli is going on a bike ride to visit Beth. He rides at 14 miles
per hour. At the same time, Beth drives her moped at 30 miles per hour to visit Eli. When will they be 1.5
miles apart?
Step 1
Draw a diagram.
Step 2
Let t = the time when they are 1.5 miles
apart. Make a table.
Eli
Beth
Step 3
r
14
30
t
t
t
d = rt
14t
30t
Write and solve an equation.
Distance traveled
by Eli
14t
14t + 30t = 14
44t = 14
44t 14
44 = 44
t  0.32
plus
distance traveled
by Beth
+
30t
equals
=
14 miles
14
Original equation
Simplify.
Divide each side by 44.
Simplify.
Eli and Beth will be 1.5 miles apart after approximately 0.32 hour, or about 19 minutes.