Difference between revisions of "2010 AMC 8 Problems/Problem 21"

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==Solution==
 
==Solution==
  
Let <math>x</math> be the number of pages in the book. After the first day, Hui had <math>4x/5-12</math> pages left to read. After the second, she had <math>(3/4)(4x/5-12]-15 = 3x/5-24</math> left. After the third, she had <math>(2/3)(3x/5-24]-18=2x/5-34</math> left. This is equivalent to <math>62.</math>
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Let <math>x</math> be the number of pages in the book. After the first day, Hui had <math>4x/5-12</math> pages left to read. After the second, she had <math>(3/4)(4x/5-12)-15 = 3x/5-24</math> left. After the third, she had <math>(2/3)(3x/5-24)-18=2x/5-34</math> left. This is equivalent to <math>62.</math>
  
 
<cmath>\begin{align*} \frac{2x}{5}-34&=62\\
 
<cmath>\begin{align*} \frac{2x}{5}-34&=62\\

Revision as of 22:17, 17 November 2011

Problem

Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read $1/5$ of the pages plus $12$ more, and on the second day she read $1/4$ of the remaining pages plus $15$ pages. On the third day she read $1/3$ of the remaining pages plus $18$ pages. She then realized that there were only $62$ pages left to read, which she read the next day. How many pages are in this book?

$\textbf{(A)}\ 120 \qquad\textbf{(B)}\ 180\qquad\textbf{(C)}\ 240\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 360$

Solution

Let $x$ be the number of pages in the book. After the first day, Hui had $4x/5-12$ pages left to read. After the second, she had $(3/4)(4x/5-12)-15 = 3x/5-24$ left. After the third, she had $(2/3)(3x/5-24)-18=2x/5-34$ left. This is equivalent to $62.$

\begin{align*} \frac{2x}{5}-34&=62\\ 2x - 170 &= 310\\ 2x &= 480\\ x &= \boxed{\textbf{(C)}\ 240} \end{align*}

See Also

2010 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions