2011 AMC 12A Problems/Problem 3: Difference between revisions
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A small bottle of shampoo can hold <math>35</math> milliliters of shampoo, whereas a large bottle can hold <math>500</math> milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy? | A small bottle of shampoo can hold <math>35</math> milliliters of shampoo, whereas a large bottle can hold <math>500</math> milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy? | ||
== Solution == | <math> | ||
To find how many small bottles we need, we can simply divide <math>500</math> by <math>35</math>. This simplifies to <math>\frac{100}{7}=14 | \textbf{(A)}\ 11 \qquad | ||
\textbf{(B)}\ 12 \qquad | |||
\textbf{(C)}\ 13 \qquad | |||
\textbf{(D)}\ 14 \qquad | |||
\textbf{(E)}\ 15 </math> | |||
== Solution 1 == | |||
To find how many small bottles we need, we can simply divide <math>500</math> by <math>35</math>. This simplifies to <math>\frac{100}{7}=14 \frac{2}{7}. </math> Since the answer must be an integer greater than <math>14</math>, we have to round up to <math>15</math> bottles, or <math>\boxed{\textbf{E}}</math> | |||
== Solution 2 == | |||
We double <math>35</math> to get <math>70.</math> We see that <math>70\cdot7=490,</math> which is very close to <math>500.</math> Thus, <math>2\cdot7+1=\boxed{\text{(E)} 15}</math> bottles are enough. | |||
~Technodoggo | |||
==Video Solution== | |||
https://youtu.be/A6oQF25ayzo | |||
~savannahsolver | |||
== See also == | == See also == | ||
{{AMC12 box|year=2011|num-b=2|num-a=4|ab=A}} | {{AMC12 box|year=2011|num-b=2|num-a=4|ab=A}} | ||
{{AMC10 box|year=2011|num-b=1|num-a=3|ab=A}} | |||
{{MAA Notice}} | |||
Latest revision as of 17:56, 10 August 2023
Problem
A small bottle of shampoo can hold 
milliliters of shampoo, whereas a large bottle can hold 
milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
Solution 1
To find how many small bottles we need, we can simply divide by . This simplifies to 
Since the answer must be an integer greater than 
, we have to round up to 
bottles, or 
Solution 2
We double to get 
We see that 
which is very close to 
Thus, 
bottles are enough.
~Technodoggo
Video Solution
~savannahsolver
See also
| 2011 AMC 12A (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 12 Problems and Solutions | |
| 2011 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 | ||
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