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Difference between revisions of "2014 AMC 12B Problems/Problem 2"

(Created page with "==Problem== Orvin went to the store with just enough money to buy <math> 30 </math> balloons. When he arrived he discovered that the store had a special sale on balloons: buy <m...")
 
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==Solution==
 
==Solution==
  
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If every balloon costs <math>n</math> dollars, then Orvin has <math>30n</math> dollars.  For every balloon he buys for <math>n</math> dollars, he can buy another for <math> \frac{2n}{3}</math> dollars.  This means it costs him <math> \frac{5n}{3}</math> dollars to buy a bundle of <math>2</math> balloons.  With <math>30n</math> dollars, he can buy <math>\frac{30n}{\frac{5n}{3}} = 18</math> sets of two balloons, so the total number of balloons he can buy is <math>18 * 2 = 36 \implies \boxed{\textbf{(C)}}</math>
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If every balloon costs <math>n</math> dollars, then Orvin has <math>30n</math> dollars.  For every balloon he buys for <math>n</math> dollars, he can buy another for <math> \frac{2n}{3}</math> dollars.  This means it costs him <math> \frac{5n}{3}</math> dollars to buy a bundle of <math>2</math> balloons.  With <math>30n</math> dollars, he can buy <math>\frac{30n}{\frac{5n}{3}} = 18</math> sets of two balloons, so the total number of balloons he can buy is <math>18 * 2 \implies \boxed{\textbf{(C)}\ 36 }</math>
  
 
Solution by kevin38017
 
Solution by kevin38017

Revision as of 16:15, 20 February 2014

Problem

Orvin went to the store with just enough money to buy $30$ balloons. When he arrived he discovered that the store had a special sale on balloons: buy $1$ balloon at the regular price and get a second at $\frac{1}{3}$ off the regular price. What is the greatest number of balloons Orvin could buy?

$\textbf{(A)}\ 33\qquad\textbf{(B)}\ 34\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}}\ 38\qquad\textbf{(E)}\ 39$ (Error compiling LaTeX. Unknown error_msg)

Solution

If every balloon costs $n$ dollars, then Orvin has $30n$ dollars. For every balloon he buys for $n$ dollars, he can buy another for $\frac{2n}{3}$ dollars. This means it costs him $\frac{5n}{3}$ dollars to buy a bundle of $2$ balloons. With $30n$ dollars, he can buy $\frac{30n}{\frac{5n}{3}} = 18$ sets of two balloons, so the total number of balloons he can buy is $18 * 2 \implies \boxed{\textbf{(C)}\ 36 }$

Solution by kevin38017

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