121 calculate number of students

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ern5231: Master | Next Rank: 500 Posts; Posts: 226; Joined: Sun Aug 09, 2009 4:34 am

by ern5231 » Mon Oct 05, 2009 8:05 pm

Last year, the Faculty to Students Ratio was is 1: 13. This year Faculty count increased by 14 and students increased by 74. The ratio now becomes 1: 12. How many students are present this year?

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Source: Beat The GMAT — Problem Solving | Mon Oct 05, 2009 8:05 pm

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Re: 121 calculate number of students

by Brent@GMATPrepNow » Mon Oct 05, 2009 8:26 pm

ern5231 wrote:Last year, the Faculty to Students Ratio was is 1: 13. This year Faculty count increased by 14 and students increased by 74. The ratio now becomes 1: 12. How many students are present this year?

Let F = # of faculty members last year
Let S = #of students last year

"Last year, the Faculty to Students Ratio was is 1: 13" --> F/S = 1/13

"This year Faculty count increased by 14 and students increased by 74. The ratio now becomes 1: 12" --> (F+14)/(S+24) = 1/12

We have a system of equations that we can solve for F and S
F/S = 1/13
(F+14)/(S+74) = 1/12

F=94
S=1222

Note These are the numbers from last year.
This year's student population is 1222+74 = 1296

Brent Hanneson - Creator of GMATPrepNow.com

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