Bunuel wrote:

At a certain university, the dormitory policy is that each dormitory must have at least 7 resident advisers for every 200 residents. If a dormitory is home to 3500 residents, what is the minimum number of resident advisers required?

A. 120

B. 121

C. 122

D. 123

E. 124

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:If the minimum ratio of resident advisers to residents is 7:200, and the dormitory has 3500 advisers, then you can set up an equation using the idea that:

The ratio of x:3500 must be greater than or equal to 7:200.

Which, mathematically, translates to:

x/3500≥7/200

Then you can cross-multiply and solve for x:

200x≥7(3500) (Note: don't actually do the multiplication when you know you'll be able to divide both sides by 100)

That reduces to:

2x≥7(35)

Which then becomes:

x≥7(35)/2

From this point you can crunch the numbers however you like. One method is to divide the 35 by 2 so that you're multiplying 7 by 17.5, which breaks out somewhat conveniently to:

7 times 10, which you know is 70.

Plus 7 times 7, which you know is 49.

Plus 7 times .5, which is 3.5.

Add those up and x must be greater than (or equal to) 122.5, but since resident advisers must be integers the answer is then 123.

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