3.9 Proportions
• Goal to solve word problems involving
proportions
Vocabulary
ratio: a comparison of two numbers
through division often expressed as a
fraction.
Proportion: An equation that states that two
ratios are equal
2 6

3 9
5 25

7 35
x 2

24 3
9 32

y 81
To Solve Proportions…
• Cross multiply and set their products = to
each other
• Ex: a = b
•
c
d
• so ad = cb
Ex 1:
3 12

5 y
y = 20
Ex 2:
x 7

4 6
14
x
3
Ex 3:
 x  5 9

3
4
4 x  20  27
4x  7
7
x
4
When to set up a proportion
• Comparing units
• Converting units
• Has the word “per”, “ratio”, “rate”, or
“out of”
Steps to Solving Word Problems
involving Proportions
1. Read the word problem twice
2. Identify the comparison of units and write
the units in fraction form
3. Set up your proportion keeping units in
proper place (convert units if need be)
4. Cross multiply
5. Set products equal to each other
6. Solve for the variable
Ex 4: On a road map 3 inches represents
40 miles. If two cities are 10 inches
apart on the map, how many miles is it
from one to the other?
inches
miles
3"
10"

40mi
d
3d  400
1
133 miles
3
Ex 5: The ratio of boys to girls on the
swim team is 5 to 4. How many girls are
on the team if there are 65 boys?
boys
girls
5 65

4
x
5 x  260
x  52 girls
Ex 6: Ryan can type 4 pages in 15
minutes. At this rate, how many pages
can he type in 2 hours?
Pages
min utes
60 min  1hour
120 min  2hours
4
x

15 120
480  15x
x  32 pages
Ex 7: A survey found that 60 out of every 85
people in a city take public transportation to
work. Out of 595 people, how many take
public transportation to work?
public  transportation
total  people
60
x

85 595
85x  35,700
x  420 people
take
public
transportation
Assignment
Page 150 (10-24 even and 25-38 all )