L.85 Proportions
Do these ratios form a proportion? Use the Constant (K Factor) to solve this.
4/10 and 12/30
Yes! Example: K factor is 3 when moving from 4/10 to 12/30.
K factor is 1/3 when moving from 12/30 to 4/10.
Solve. Be sure to show your evidence.
6/8 as n/20
n = 15
Ex: 6(20) = 120/8 = 15
The ratio of football players to band members is 2 to 5. Altogether, there were 175 people in the 2 groups. How many football players would be present?
(Get 6 positions down to 4 for a proportion!)
50 football players
2/7 = f/175
175(2)= 350/7 = 50
If a crop circle has a radius of 12km, how big would its "measuring box" be? Show your work!
144 sq km
12(12) = 144
Using cross products, prove that these ratios are proportional or not.
4/12 and 5/15
Yes proportional. 4 x 15 = 60 and 5 x 12 = 60
Solve. Be sure to show your evidence.
6/3.9 = 10/c
c = 6.5
10(3.9) = 39/6 = 6.5
The ratio of windows to doors in a classroom was 5 to 4. If there were 27 total (including both), how many doors would this be?
(6 positions needs to be made into 4 to make a proportion)
12 doors
4/9 = D/27
k factor = 3
4(3) = 12
A circular trampoline has a diameter of 12 feet across. What is its area? Show your work! (Use 3.14 for pi)
113.04 sq ft
A = 3.14(6^2)
A = 3.14(36)
Use cross products to prove that these ratios are proportional or not.
93/60 and 62/40
Yes they're proportional.
93(40) = 3720
62(60) = 3720
12/n = 4/21
Solve and include evidence!
n = 63
k factor from 4/21 to 12/n is 3
21(3) = 63
The ratio of boys to girls in the theater was 3 to 2. If there were 300 students in the theater, how many girls would there be?
(6 positions need to be made into 4 to make a proportion)
120 girls
2/5 = G/300
k factor = 60
2(60) = 120
An Aztec Calendar was circular and measured 26 cm all the way across through its center point. How big would its measuring box be? What would its area be? (Show your work!)
169 sq cm = measuring box
area = 530.66 sq cm
26 diameter = 13 radius; 13(13) = 169
3.14(169) = 530.66
Use whatever method you wish to prove proportionality or not. Include your evidence!
6.1/3.4 and 7.4/4.7
Not proportional.
cross products = 28.67 and 25.16
A poster is printed from a photo. The photo is 4in wide and 6in long. If the poster is proportional and 22 inches wide, how long would it be? Show your evidence!
33 inches
Ex: Fish Method = 22(6) = 132/4 = 33
Thirty percent of the cars in a parade are antiques. If 12 vehicles are antiques, how many total cars were in the parade?
(Use a proportion to solve this.)
40 total cars
30/100 = 12/T
Fish = 12(100) = 1200/30 = 40
Campers arrange rocks in a circle that's 14 feet across for their campsite. If their group included 4 campsites, how much area would this be total? (Show your work!)
615.44 sq feet
diameter = 14, radius = 7
7(7) = 49(3.14) = 153.86
153.86(4 campsites) = 615.44
Suppose a/b forms a proportion with m/n, but does not form a proportion with x/y. Does m/n form a proportion with x/y?
Use an example to prove your answer!
No m/n is not proportional to x/y.
Example: a/b = 1/2
m/n = 2/4; x/y = 3/7
therefore 1/2 = 2/4, but 2/4 does not = 3/7
Chris earns $25 for 3 hours of work. How much would he make at this rate if he worked 5 hours? Round your answer to the nearest cent. Show your work!
$41.67
25/3 = 41.67/5
Cross products = approx. 125
85% of students were present on Friday. If there are 60 students in the group, how many were absent? Show your proportion!
9 were absent
15/100 = A/60
Fish = 60(15) = 900/100 = 9
The circumference of a kiddie pool is 47.1 feet. What is its area? Round your final answer to the nearest whole number. (Show your work!)
177 sq feet
C = pi (d)
47.1 = 3.14 (d)
47.1/3.14 = 15; diameter 15 = 7.5 radius
7.5(7.5) = 56.25(3.14) = 176.625