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Bunuel
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 19 Feb 2015, 09:37
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

86% (02:10) correct 14% (02:38) wrong based on 169 sessions

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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron is 7 years older than Ken. If the sum of the ages of all four people is 161, how many years old is Ron?

A. 15
B. 19
C. 22
D. 24
E. 27
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C
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 19 Feb 2015, 09:57
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Ben = B, Ron = R, Ken = K, Ed = E

B = 3R
E = B - 8 = (3R - 8)
K = R - 7

B + R + K + E = 161
3R + R + (R - 7) + (3R - 8) = 161
8R - 15 = 161
8R = 176
R = 22

The correct answer is C.
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 22 Feb 2015, 12:28
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Bunuel
Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron is 7 years older than Ken. If the sum of the ages of all four people is 161, how many years old is Ron?

A. 15
B. 19
C. 22
D. 24
E. 27

MAGOOSH OFFICIAL SOLUTION
Attachment:
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 22 Feb 2015, 22:34
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Hi All,

While most Test Takers would solve this with Algebra (which is fine), you might find it easier/faster to TEST THE ANSWERS.

We're given a number of facts about the relative ages of 4 people:
1) Ben is 3(Ron)
2) Ed is 8 years younger than Ben
3) Ron is 7 years older than Ken
4) The sum of the ages is 161

We're asked how old RON is. The information is in the perfect order to START with Ron, then calculate everyone else.

Let's TEST Answer B first....
IF....
Ron = 19
Ben = 3(19) = 57
Ed = 49
Ken = 12
Total = 19 + 57 + 49 + 12 = 137. This is TOO LOW (it's supposed to be 161), so everyone needs to be OLDER.

Now let's TEST Answer D....
IF...
Ron = 24
Ben = 3(24) = 72
Ed = 64
Ken = 17
Total = 24 + 72 + 64 + 17 = 177. This is TOO HIGH.

The correct answer MUST be between Answers B and D.

Final Answer:
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C

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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 24 Feb 2015, 21:50
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Answer = C = 22

Ages ................... Ben .................... Ron .................... Ed .................. Ken

.......................... 3x .......................... x ....................... 3x-8 .............. x-7

3x+x+3x-8+x-7 = 161

x = 22
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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 28 Feb 2015, 07:53
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Bunuel
Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron is 7 years older than Ken. If the sum of the ages of all four people is 161, how many years old is Ron?

A. 15
B. 19
C. 22
D. 24
E. 27

Given that,
B = 3R
E = B - 8
R = 7 + K
B + E + R + K = 161
We want the answer in terms of Ron.
So, (3R) + (3R - 8) + R + (R - 7) = 161
8R = 176
Hence R = 22
Hence option C.

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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron 02 Oct 2016, 11:40
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I got this question wrong when I first did it. When I did it again I got it right. This problem is duable if you keep calm, no exclamation marks.

Algebraic way:

step1: organize what the stem is giving you into equations and mark what they are asking you to solve. You are looking for R.
3R = B
E+8 = B
K + 7 = R
R + B + E + K = 161

step2: find out how to get R. If you see at the equations. you can re-write all in R terms.
3R = B
E+8 = B => E+8=3R => E = 3R - 8
K + 7 = R => K = R-7
R + B + E + K = 161 => R + 3R + 3R -8 + R-7 = 161 => R = 22

Additional comment: When I did it first I took too long because i did not organize well. Then the combo was that I substracted 161 - 15 when I should have added 161+15. The point comes down to keeping calm. Organization of ideas improves if I keep calm.
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Bunuel
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