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Difference between revisions of "2007 AMC 8 Problems/Problem 7"

(Created page with '== Problem == The average age of <math>5</math> people in a room is <math>30</math> years. An <math>18</math>-year-old person leaves the room. What is the average age of the fou…')
 
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The answer is <math>\boxed{D}</math>
 
The answer is <math>\boxed{D}</math>
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OR
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Since an <math>18</math> year old left from a group of people averaging <math>30</math>, The remaining people must total <math>30 - 18 = 12</math> years older than <math>30</math>. Therefore, the average is <math>\frac{12}{4} = 3</math> years over <math>30</math>. Giving us <math>33</math>. <math>\boxed{D}</math>

Revision as of 17:00, 15 February 2010

Problem

The average age of $5$ people in a room is $30$ years. An $18$-year-old person leaves the room. What is the average age of the four remaining people?

$\mathrm{(A)}\ 25 \qquad\mathrm{(B)}\ 26 \qquad\mathrm{(C)}\ 29 \qquad\mathrm{(D)}\ 33 \qquad\mathrm{(E)}\ 36$

Solution

Let $x$ be the average of the remaining $4$ people.

The equation we get is $\frac{4x + 18}{5} = 30$

Simplify,

$4x + 18 = 150$

$4x = 132$

$x = 33$

The answer is $\boxed{D}$


OR


Since an $18$ year old left from a group of people averaging $30$, The remaining people must total $30 - 18 = 12$ years older than $30$. Therefore, the average is $\frac{12}{4} = 3$ years over $30$. Giving us $33$. $\boxed{D}$

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