Big Idea
Proportions can be solved
algebraically using the Means-Extremes Property.
Means-Extremes Property
For all real numbers a, b, c, and d
(with b and d not zero), if a = c
then ad = bc. b d
Goal
Justify and use the Means-Extremes
Property in solving proportions.
Warm-Up
1. If you are charged $1.69 for
3 cans of peaches, how much
should you expect to pay for
8 cans?
2. If in traffic it takes a bus 5
minutes to travel ¾ of a mile,
how long at that rate would it
take the bus to travel 6 miles?
3. Booker is reading a 300page novel. It has taken him 2
hours to read the first 72
pages. At this rate, how many
more hours will it take him to
finish the novel?
1. 1.69 = x
3
8
3x = 1.69 · 8
3x = 13.52
3
3
x = $4.51
2. 5 = x
¾ 6
3x = 5 · 6
4
4  3x = 30  4
3 4
1 3
x = 40 min.
3. 2 = x
72 300-72
72x = 2 · 228
72x = 456
72
72
x = 6⅓ hr. more
Additional Examples
1. 5 = 9
1. Complete the sentence, “5 is
15 x
to 15 as 9 is to _____.”
5x = 15 · 9
5x = 135
2. A survey of 200 high school
5
5
students found that 145 of them
x = 27
had their own television set.
Based on the results of this
survey, about how many
students in a school of 3,175
would have their own television
3. Let x = Eric
set?
2. 145 = x
200 3175
200x = 145·3175
200x = 460375
200
200
x = 2,302 st.
then Leslie = x - .8
x = 11
3. Two runners, Eric and Leslie,
x - .8 10
competed in a race. Eric’s time
was 0.8 minute slower than
10x = 11(x - .8)
Leslie’s. Their times were in the 10x = 11x – 8.8
ratio of 11 to 10. What was
-(-1x = -8.8)
-11x -11x
Eric’s time?
x = 8.8 min.
-1x = -8.8