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
Can some experts show me the simplest solution?
OA D
At a certain university
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Let a = the number of advisers.lheiannie07 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
Since there are 3500 residents -- and the ratio of advisers to residents must be at least 7/200 -- we get:
a/3500 ≥ 7/200
200a ≥ 3500*7
2a ≥ 35*7
2a ≥ 245
a ≥ 122.5.
Since the value of a must be an INTEGER, the least possible value for a is 123.
The correct answer is D.
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We can create the following proportion where n is the number of resident advisers:lheiannie07 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
n/3500 ≥ 7/200
200n ≥ 7 x 3500
2n ≥ 7 x 35
n ≥ 122.5
Thus, the minimum value of n is 123.
Answer: D
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