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

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Joined: 02 Sep 2009
Posts: 58464
For every administrator at a certain summer program there are two coun  [#permalink]

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28 Dec 2017, 21:36
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:30) correct 40% (01:30) wrong based on 45 sessions

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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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Re: For every administrator at a certain summer program there are two coun  [#permalink]

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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
.
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Re: For every administrator at a certain summer program there are two coun  [#permalink]

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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]

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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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