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For every administrator at a certain summer program there are two coun

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Bunuel
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For every administrator at a certain summer program there are two coun [#permalink] New post   28 Dec 2017, 21:36
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For every administrator at a certain summer program there are two counselors and for each counselor there are 7 children. If all of the 170 people at the program go to an amusement park, how many counselors went to the park?

A. 10
B. 17
C. 20
D. 34
E. 119
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C
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DavidTutorexamPAL
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Re: For every administrator at a certain summer program there are two coun [#permalink] New post   29 Dec 2017, 04:47
Bunuel wrote:
For every administrator at a certain summer program there are two counselors and for each counselor there are 7 children. If all of the 170 people at the program go to an amusement park, how many counselors went to the park?

A. 10
B. 17
C. 20
D. 34
E. 119


We'll translate our question into algebra in order to solve the question.
This is a Precise approach.

The ratio between administrators to counselors is 1:2 and between counselors to children is 1:7.
To compare these we'll multiply the second ratio by 2 giving a ratio of 2:14 between counselors to children.
Our total ratio is 1:2:14 which combine for a total of 1+2+14 = 17 'ratio units'.
Since 170 people went ot the amusement park, each ratio unit is worth 170/17 = 10.
There are 2 ratio units of counselors giving a total of 10*2 = 20 counselors
.
(C) is our answer.
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Re: For every administrator at a certain summer program there are two coun [#permalink] New post   07 Apr 2019, 11:25
Bunuel wrote:
For every administrator at a certain summer program there are two counselors and for each counselor there are 7 children. If all of the 170 people at the program go to an amusement park, how many counselors went to the park?

A. 10
B. 17
C. 20
D. 34
E. 119


total ratio admin:councilar:children ; 1:2:14 = 170
or say 17x=170
x=10
so councilors = 2*10 ; 20
IMO C
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Re: For every administrator at a certain summer program there are two coun [#permalink] New post   07 Apr 2019, 17:20
Bunuel wrote:
For every administrator at a certain summer program there are two counselors and for each counselor there are 7 children. If all of the 170 people at the program go to an amusement park, how many counselors went to the park?

A. 10
B. 17
C. 20
D. 34
E. 119


Let number of administrators be\(x\).
No of counselors=\(2*x\)
No of children=\(7*2*x=14x\)

Total number of people=\(x+2x+14x=17x=170\)
\(x=10\).
No of counselors= \(2*10=20\). IMO, Option C.
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Re: For every administrator at a certain summer program there are two coun [#permalink]
07 Apr 2019, 17:20
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