A ratio, which is a comparison of 2 quantities, assists with making wise decisions. Perhaps you’ll sign a 2-year contract with the cell phone company that offers the lowest costs per text message (ratio: dollar/text message). Perhaps you’re trying to predict how much sugar you’ll need to add to a fruit punch that serves a dozen people (ratio: pounds of sugar/people).
But let’s get real: most of us flee the rationale of ratios.
You’re probably going to do business with the cell phone company that offers you the flashiest phone. And if you’re anything like me, you’ll sweeten that diabetes punch with enough sugar to energize a sloth.
Unfortunately, you can’t hide from ratios on the PSAT, SAT, or ACT. This article focuses on a skill that is tested on these entrance exams: how to use ratios to make predictions.
How to Write a Ratio
Let’s say that there are 8 girls and 5 boys in a classroom.
Part to Part Ratio
- What is the ratio of girls to boys? 8 to 5 or 8:5 or 8/5
- What is the ratio of boys to girls? 5 to 8 or 5:8 or 5/8
Part to Whole Ratio
- What is the ratio of girls to total number of students? 8 to 13 or 8:13 or 8/13
- What is the ratio of boys to the total number of students? 5 to 13 or 5:13 or 5/13
Predictions: Use a Part of a Ratio to Find Another Part
The ratio of boys to girls in a classroom is 5 to 8. Ten boys attend Ms. Thompson's English class. How many girls are in the class?
Ratio: 5 boys + 8 girls = 13 students in the classroom
Actual: 10 boys + g girls = t total students in the classroom
Set up a proportion.
5/8 = 10/g
Cross-multiply to solve.
5*g = 10 * 8
5g = 80
5g/5 = 80/5
g = 16
16 girls
Predictions: Using the Whole of Ratio to Find a Part
John attends Zoology class in a large lecture hall. The ratio of female to male students in the class is 9:4. If there are 468 students in the lecture hall, then how many male students are there?
Ratio: 9 female students + 4 male students = 13 total students
Actual: f female students + m male students = 468 total students
Set up a proportion.
4/13 = m/468
Cross-multiply to solve.
4* 468 = m * 13
1872 = 13m
1872/13 = 13m/13
144 = m
Answers and Explanations
1. In America, the ratio of poor children to total children is 1:6. If there are 7,788 children in Lochester, a small American city, then how many children live in poverty in Lochester? There are 1,298 poor children in Lochester.
Ratio: 1 poor child + 5 non-poor children = 6 total children
Actual: p poor children + n non-poor children = 7,788 total children
Set up a proportion.
1/6 = p/7,788
Cross-multiply to solve.
1 * 7,788 = p * 6
7,788 = 6p
7,788/6 = 6p/6
1298 = p
There are 1,298 poor children in Lochester.
2. In America, the ratio of impoverished children to non-impoverished children is 1:5. In Jochester, a city in America, 60,500 children live above the poverty level. How many children in this town live below the poverty level? In Jochester, 12,100 children live below the poverty level.
Ratio: 1 child in poverty + 5 children above poverty level = 6 total children
Actual: p children in poverty + 60,500 children above poverty level = t total children
Set up a proportion.
1/5 = p/60,500
Cross-multiply to solve.
1 * 60,500 = p * 5
60,500 = 5p
60,500/5 = 5p/5
12,100 = p
In Jochester, 12,100 children live below the poverty level.
3. At Oliver High School, the ratio of students to teachers is 320:3. If there are going to be 4,100 students enrolled this year, then how many teachers will Oliver High need? Oliver High will need about 38 teachers.
Ratio: 320 students: 3 teachers
Actual: 4,100 students : t teachers
Set up a proportion.
320/3 = 4100/t
Cross-multiply to solve.
320 * t = 4100 * 3
320t = 12300
320t/320 = 12300/320
t = 38.4375
Oliver High will need about 38 teachers.
4. At Sanger Preparatory Academy, the ratio of students to teachers is 45:4. How many teachers will the school need if 392 students attend? Sanger Preparatory Academy will need about 35 teachers.
Ratio: 45 students : 4 teachers
Actual: 392 students : t teachers
Set up a proportion.
45/4 = 392/t
Cross-multiply to solve.
45 * t = 392 * 4
45t = 1568
45t/45 = 1568/45
t = 34.8444
Sanger Preparatory Academy will need about 35 teachers.
5. At the football game, 16 students crowd in a 20 square foot space to watch the game at the stadium in the student section.
A. What is the ratio of students to square feet?
16:20 or 4:5
B. If there are 17,500 students watching the game from the student section, how many square feet do they occupy?
Ratio: 16 students : 20 square feet
Actual: 17,500 students : s square feet
Set up a proportion.
16/20 = 17,500/s
16 * s = 17,500 * 20
16s = 350,000
16s/16 = 350,000/16
s = 21,875
The students occupy 21,875 square feet.