Question

solving word problems
with proportions
name
directions: set up a proportion for each problem. then, solve it by using cross products. show
your steps, and label your answers.
example:
during a dodgeball game, ms. hodovance threw
the ball 10 times, and hit 4 students. if her
average stays the same, how many times does
she have to throw the ball to hit 14 students?
units:
$\frac{throws}{students hit}$ $\frac{10 throws}{4 students} = \frac{t}{14 students}$
write cross products: $4t = 10 \bullet 14$
multiply: $4t = 140$
undo/divide: $\frac{4t}{4} = \frac{140}{4}$
solution: $t = 35 throws$

1. carol spends 17 hours in a 2-week period

practicing her clarinet. how many hours does
she practice in 5 weeks?
units:

1. in a shipment of 400 parts, 14 are found to be

defective. how many defective parts should be
expected in a shipment of 1000 parts?
units:

1. joey can type 80 words per minute. how

many words can he type in 30 minutes?
units:

1. eight oranges cost $1.00. how much will 5

dozen oranges cost?

1. a certain shade of paint is made by mixing 5

parts blue paint with 2 parts white paint. to get
the correct shade, how many quarts of white
paint should be mixed with 8.5 quarts of blue
paint?

1. a 12-pack of 8-ounce juice boxes costs $5.40.

how much would an 18-pack of juice boxes cost if
it is proportionate in price?

Explanation:

Problem 1

Step1: Define proportion units

Units: $\frac{\text{hours}}{\text{weeks}}$

Step2: Set up proportion

$\frac{17}{2} = \frac{h}{5}$

Step3: Cross multiply

$2h = 17 \times 5$

Step4: Calculate and isolate h

$2h = 85$
$h = \frac{85}{2} = 42.5$

Problem 2

Step1: Define proportion units

Units: $\frac{\text{defective parts}}{\text{total parts}}$

Step2: Set up proportion

$\frac{14}{400} = \frac{d}{1000}$

Step3: Cross multiply

$400d = 14 \times 1000$

Step4: Calculate and isolate d

$400d = 14000$
$d = \frac{14000}{400} = 35$

Problem 3

Step1: Define proportion units

Units: $\frac{\text{words}}{\text{minutes}}$

Step2: Set up proportion

$\frac{80}{1} = \frac{w}{30}$

Step3: Cross multiply

$1 \times w = 80 \times 30$

Step4: Calculate total words

$w = 2400$

Problem 4

Step1: Convert to consistent units

5 dozen = $5 \times 12 = 60$ oranges

Step2: Define proportion units

Units: $\frac{\text{cost}}{\text{oranges}}$

Step3: Set up proportion

$\frac{1.00}{8} = \frac{c}{60}$

Step4: Cross multiply

$8c = 1.00 \times 60$

Step5: Calculate and isolate c

$8c = 60$
$c = \frac{60}{8} = 7.50$

Problem 5

Step1: Define proportion units

Units: $\frac{\text{blue paint}}{\text{white paint}}$

Step2: Set up proportion

$\frac{5}{2} = \frac{8.5}{w}$

Step3: Cross multiply

$5w = 2 \times 8.5$

Step4: Calculate and isolate w

$5w = 17$
$w = \frac{17}{5} = 3.4$

Problem 6

Step1: Define proportion units

Units: $\frac{\text{cost}}{\text{number of packs}}$

Step2: Set up proportion

$\frac{5.40}{12} = \frac{p}{18}$

Step3: Cross multiply

$12p = 5.40 \times 18$

Step4: Calculate and isolate p

$12p = 97.2$
$p = \frac{97.2}{12} = 8.10$

Answer:

1. 42.5 hours
2. 35 defective parts
3. 2400 words
4. $7.50
5. 3.4 quarts
6. $8.10