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. Xavier is applying to Dream University. Each student who applies to the school takes either the SAT or ACT. Last year, for every 4 applicants who took the SAT, 3 other students took the ACT. The total number of applicants was 28,000. How many students took the SAT? 16,000 students
Ratio: 4 SAT students + 3 ACT students = 7 total students
Actual: s students + a ACT students = 28,000 students
Set up a proportion.
4/7 = s/28,000
Cross-multiply to solve.
4 * 28,000 = 7 * s
112,000 =7s
112,000/7 = 7s/7
16,000 = s
16,000 students
2. At Dream University, freshmen are encouraged, but not required, to live in the campus residence halls. Otherwise, the first-year college students commute to campus. The ratio of on-campus freshmen to commuter freshmen is 20 to 1. If 42 freshmen commute, then how many freshmen live on campus? 840 freshmen live on campus.
Ratio: 20 on-campus freshmen + 1 commuter freshman = 21 total freshmen
Actual: n on-campus freshmen + 42 c commuter freshmen = t total freshmen
Set up a proportion.
20/1 = n/42
Cross-multiply to solve.
20 * 42 = n *1
840 = 1n
840 = n
840 freshmen live on campus.
3. Lin is shopping for an American History textbook. The bookstore carries new and used versions of the book. The ratio of new to used books is 25:4. If there are 500 American History textbooks in stock, then how many used books are available? About 69 used textbooks
Ratio: 25 new books + 4 used books = 29 total books
Actual: n new books + u used books = 500 total books
Set up a proportion.
4/29 = u/500
Cross-multiply to solve.
4 * 500 = u * 29
2000 = 29u
2000/29 = 29u/29
68.97 = u
About 99 used textbooks
4. An online company, farmerandfriends.org, only accepts debit or credit cards for its transactions. The ratio of debit card to credit card use is 3 dollars to 5 dollars. If farmerandfriends.org recorded $7,500 in monthly transactions, then how much money came from credit card transactions? $4,687.50 in credit card transactions
Ratio: $3 in debit transactions + $5 in credit transactions = 8 total transactions
Actual: d dollars in debit transactions + c dollars in credit transactions = $7,500 total
Set up a proportion.
5/8 = c/7500
Cross-multiply to solve.
5 * 7500 = c * 8
37500 = 8c
37500/8 = 8c/8
4687.50 = c
$4,687.50 in credit card transactions
5. A movie theater sells children's tickets for $5 and adults' tickets for $10. The ratio of children to adult tickets sold in the month of June is 3:20.
A. If the total number of tickets sold was 2,760, then how many children’s tickets were sold? 360 children’s tickets
Ratio: 3 children’s tickets + 20 adults' tickets = 23 total tickets
Actual: c children’s tickets + a adults' tickets = 2,760 tickets
Set up a proportion.
3/23 = c/2760
Cross-multiply to solve.
3* 2760 = c * 23
8280 = 23c
8280/23 = 23c/23
360 = c
360 children’s tickets
B. How much revenue did the movie theater earn from adult tickets? $24,000 revenue from adult tickets
2,760 total tickets – 360 children’s tickets = 2400 adult tickets
Each adult ticket costs $10
2400 * 10 = $24,000 revenue from adult tickets