Difference between revisions of "2010 AMC 8 Problems/Problem 21"
m (brackets) |
(→Solution 2(working backwards)) |
||
| (14 intermediate revisions by 11 users not shown) | |||
| Line 4: | Line 4: | ||
<math> \textbf{(A)}\ 120 \qquad\textbf{(B)}\ 180\qquad\textbf{(C)}\ 240\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 360 </math> | <math> \textbf{(A)}\ 120 \qquad\textbf{(B)}\ 180\qquad\textbf{(C)}\ 240\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 360 </math> | ||
| − | ==Solution== | + | ==Solution 1(algebra solution)== |
| − | Let <math>x</math> be the number of pages in the book. After the first day, Hui had <math>4x | + | Let <math>x</math> be the number of pages in the book. After the first day, Hui had <math>\frac{4x}{5}-12</math> pages left to read. After the second, she had <math>\left(\frac{3}{4}\right)\left(\frac{4x}{5}-12\right)-15 = \frac{3x}{5}-24</math> left. After the third, she had <math>\left(\frac{2}{3}\right)\left(\frac{3x}{5}-24\right)-18=\frac{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\\ | ||
| Line 12: | Line 12: | ||
2x &= 480\\ | 2x &= 480\\ | ||
x &= \boxed{\textbf{(C)}\ 240} \end{align*}</cmath> | x &= \boxed{\textbf{(C)}\ 240} \end{align*}</cmath> | ||
| + | |||
| + | ==Video Solution by OmegaLearn== | ||
| + | |||
| + | https://youtu.be/rQUwNC0gqdg?t=1739 | ||
| + | |||
| + | ~pi_is_3.14 | ||
| + | |||
| + | ==Video by MathTalks== | ||
| + | |||
| + | https://youtu.be/mSCQzmfdX-g | ||
| + | |||
| + | |||
| + | ==Video Solution by WhyMath== | ||
| + | https://youtu.be/p2wtDPepQhY | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2010|num-b=20|num-a=22}} | {{AMC8 box|year=2010|num-b=20|num-a=22}} | ||
| + | {{MAA Notice}} | ||
Revision as of 10:00, 15 July 2024
Contents
Problem
Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read 
of the pages plus 
more, and on the second day she read 
of the remaining pages plus 
pages. On the third day she read 
of the remaining pages plus 
pages. She then realized that there were only 
pages left to read, which she read the next day. How many pages are in this book?
Solution 1(algebra solution)
Let 
be the number of pages in the book. After the first day, Hui had 
pages left to read. After the second, she had 
left. After the third, she had 
left. This is equivalent to 
Video Solution by OmegaLearn
https://youtu.be/rQUwNC0gqdg?t=1739
~pi_is_3.14
Video by MathTalks
Video Solution by WhyMath
~savannahsolver
See Also
| 2010 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
