VALENCIA MTB 1103 - Using Ratio to Compare Quantities

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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 In other words the Athletic Club boasts 4 men for each woman 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 Athletic Club 6 women 24 men Simplified 1 women 4 men Young Professionals Meeting 24 women 6 men Simplified 4 women 1 man 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 1 Calculate the ratio of applicants to full ride scholarships at College A 825 applicants 275 scholarships Simplify 3 applicants 1 scholarship 2 Calculate the ratio of applicants to full ride scholarships at College B 600 applicants 150 scholarships Simplify 4 applicants 1 scholarship 3 Calculate the ratio of applicants to full ride scholarships at College C 2 250 applicants 250 scholarships Simplify 9 applicants 1 scholarship 4 Calculate the ratio of applicants to full ride scholarships at College D 1 250 applicants 125 scholarships Simplify 10 applicants 1 scholarship 5 Which college has the least favorable applicant to scholarship ratio College D 6 Which college has the most favorable applicant to scholarship ratio College A 7 To which college will Mario apply College A


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