Optometry school applicants decreased by 25% during a 4-year period. During the same time, the number of first-year openings in optometry school increased by 12%. If the ratio of applicants to first-year student openings had been 3 to 1, then which of the following would be the approximate ratio at the end of the 4-year period? A. 1.5 to 1B. 2 to 1C. 3 to 2D. 4 to 3E. 6 to 5E. ((63.5) / (7.09)) (25)

Question

Mathematics

Joe Charles

20 August, 15:01

Optometry school applicants decreased by 25% during a 4-year period. During the same time, the number of first-year openings in optometry school increased by 12%. If the ratio of applicants to first-year student openings had been 3 to 1, then which of the following would be the approximate ratio at the end of the 4-year period? A. 1.5 to 1B. 2 to 1C. 3 to 2D. 4 to 3E. 6 to 5E. ((63.5) / (7.09)) (25)

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Abagail Foley · Answer 1

The ratio was approximately 2 to 1. Option B was correct

Step-by-step explanation:

Lets call x the number of first year students before the 4-year period. The number of applicants was 3x. After 4 years the number of applicants was reduced a 25%, hence it was multiplied by 0.75, and the number of first-years was increased a 12%, hence it was multiplied by 1.12.

New number of applicants: 3x*0.75 = 2.25x

New number of first years: x*1.12 = 1.12x

The new ratio is 2.25x/1.12x = 2.25/1.12 = 2.009, approximately 2 to 1.