Difference between revisions of "2005 AMC 10B Problems/Problem 3"
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A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day? | A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day? | ||
| − | <math>\ | + | <math>\textbf{(A) } \frac{1}{10} \qquad \textbf{(B) } \frac{1}{9} \qquad \textbf{(C) } \frac{1}{3} \qquad \textbf{(D) } \frac{4}{9} \qquad \textbf{(E) } \frac{5}{9} </math> |
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== Solution == | == Solution == | ||
| − | After the first day, there is <math>1-\left(\dfrac{1}{3}\ | + | After the first day, there is <math>1-\left(\dfrac{1}{3}\cdot1\right)=\frac{2}{3}</math> gallons left. After the second day, there is a total of <math>\dfrac{2}{3}-\left(\dfrac{1}{3}\times\dfrac{2}{3}\right)=\dfrac{2}{3}-\dfrac{2}{9}=\dfrac{4}{9}</math>. Therefore, the fraction of the original amount of paint that is left is <math>\dfrac{\dfrac{4}{9}}{1}=\boxed{\textbf{(D) }\frac{4}{9}}</math>. |
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| + | Another way to do this is just to simply find the gain everyday and subtract from the remaining you had before. | ||
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==See Also == | ==See Also == | ||
| + | {{AMC10 box|year=2005|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 13:00, 14 December 2021
Problem
A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?
Solution
After the first day, there is 
gallons left. After the second day, there is a total of 
. Therefore, the fraction of the original amount of paint that is left is 
.
Another way to do this is just to simply find the gain everyday and subtract from the remaining you had before.
See Also
| 2005 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
