To paraphrase Frederick Douglass, “We may not get all that we pay for, but we will certainly pay for all that we get.” To salute that grand arbiter of coiffure and promoter of equality, let’s discuss how to best use our resources. Use a ratio to compare two quantities.

### Examples: Using Ratio to Compare Quantities

- Miles per hour
- Text messages per dollar
- Facebook page visitors per week
- Men per women

### Example: Ratio and Social Life

Sheila, a busy career woman, plans to wisely use her leisure time. She wants a place with as many men per women as possible. As a statistician, this single woman believes that a high male to female ratio is the best way to find Mr. Right. Here are the female and male headcounts of certain places:

- Athletic Club, Thursday night: 6 women, 24 men
- Young Professionals Meeting, Thursday night: 24 women, 6 men
- Bayou Blues Night Club, Thursday night: 200 women, 300 men

Which place will Sheila choose? Calculate the ratios:

#### Athletic Club

6 women/24 men

Simplified: 1 women/4 men

In other words, the Athletic Club boasts 4 men for each woman.

#### Young Professionals Meeting

24 women/6 men

Simplified: 4 women/1 man

In other words, the Young Professionals Meeting offers 4 women for each man.

*Note*: A ratio can be an improper fraction; the numerator can be greater than the denominator.

#### Bayou Blues Club

200 women/300 men

Simplified: 2 women/3 men

In other words, for every 2 women at the Bayou Blues Club, there are 3 men.

### Which Place Offers the Best Female to Male Ratio?

Unfortunately for Sheila, the female-dominated Young Professionals Meeting is not an option. Now, she has to choose between the Athletic Club and the Bayou Blues Club.

Compare the Athletic Club and Bayou Blues Club ratios. Use 12 as the common denominator.

- Athletic Club: 1 women/4 men = 3 women/12 men
- Bayou Blues Club: 2 women/3 men = 8 women/12 men

On Thursday, Sheila wears her best spandex outfit to the male-dominated Athletic Club. Unfortunately, the four men she meets all have breath like train smoke. So much for using math in real life.

### Exercises

Mario can afford to apply to only one university. He will apply to the school that offers the best probability of awarding him a full, academic scholarship. Assume that each scholarship committee — overworked and understaffed — will award scholarships to students whose names are randomly pulled from a hat.

Each of Mario's prospective schools has posted its average number of applicants and average number of full-ride scholarships.

- College A: 825 applicants; 275 full-ride scholarships
- College B: 600 applicants; 150 full-ride scholarships
- College C: 2,250 applicants; 250 full-ride scholarships
- College D: 1,250 applicants; 125 full-ride scholarships

- Calculate the ratio of applicants to full-ride scholarships at College A.

825 applicants: 275 scholarships

Simplify: 3 applicants: 1 scholarship - Calculate the ratio of applicants to full-ride scholarships at College B.

600 applicants: 150 scholarships

Simplify: 4 applicants: 1 scholarship - Calculate the ratio of applicants to full-ride scholarships at College C.

2,250 applicants: 250 scholarships

Simplify: 9 applicants: 1 scholarship - Calculate the ratio of applicants to full-ride scholarships at College D.

1,250 applicants: 125 scholarships

Simplify: 10 applicants: 1 scholarship - Which college has the least favorable applicant to scholarship ratio?

College D - Which college has the most favorable applicant to scholarship ratio?

College A - To which college will Mario apply?

College A