Difference between revisions of "2011 AMC 12A Problems/Problem 3"

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== Problem ==
 
== Problem ==
A small bottle of shampoo can hold 35 milliliters of shampoo, whereas a large bottle can hold 500 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?
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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?
  
== Solution ==
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<math>
To find how many small bottles we need, we can simply divide 500 by 35. This simplifies to 100/7=14+2/7. Since the answer must be an integer greater than 14, we have to round up to 15 bottles=<math>\boxed{E}</math>
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\textbf{(A)}\ 11 \qquad
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\textbf{(B)}\ 12 \qquad
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\textbf{(C)}\ 13 \qquad
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\textbf{(D)}\ 14 \qquad
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\textbf{(E)}\ 15 </math>
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== Solution 1 ==
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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>
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== Solution 2 ==
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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.
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~Technodoggo
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==Video Solution==
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https://youtu.be/A6oQF25ayzo
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~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}}
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{{MAA Notice}}

Latest revision as of 17:56, 10 August 2023

Problem

A small bottle of shampoo can hold $35$ milliliters of shampoo, whereas a large bottle can hold $500$ 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?

$\textbf{(A)}\ 11 \qquad \textbf{(B)}\ 12 \qquad \textbf{(C)}\ 13 \qquad \textbf{(D)}\ 14 \qquad \textbf{(E)}\ 15$

Solution 1

To find how many small bottles we need, we can simply divide $500$ by $35$. This simplifies to $\frac{100}{7}=14 \frac{2}{7}.$ Since the answer must be an integer greater than $14$, we have to round up to $15$ bottles, or $\boxed{\textbf{E}}$

Solution 2

We double $35$ to get $70.$ We see that $70\cdot7=490,$ which is very close to $500.$ Thus, $2\cdot7+1=\boxed{\text{(E)} 15}$ bottles are enough. ~Technodoggo

Video Solution

https://youtu.be/A6oQF25ayzo

~savannahsolver

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
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 (ProblemsAnswer KeyResources)
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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