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

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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 <math> 1 </math> balloon at the regular price and get a second at <math> \frac{1}{3} </math> off the regular price. What is the greatest number of balloons Orvin could buy?
 
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 <math> 1 </math> balloon at the regular price and get a second at <math> \frac{1}{3} </math> off the regular price. What is the greatest number of balloons Orvin could buy?
  
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<math> \textbf{(A)}\ 33\qquad\textbf{(B)}\ 34\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}}\ 38\qquad\textbf{(E)}\ 39 </math>
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<math> \textbf{(A)}\ 33\qquad\textbf{(B)}\ 34\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 38\qquad\textbf{(E)}\ 39 </math>
  
 
==Solution==
 
==Solution==

Revision as of 21:39, 2 March 2015

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?

$\textbf{(A)}\ 33\qquad\textbf{(B)}\ 34\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 38\qquad\textbf{(E)}\ 39$

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 $18\times2 \implies \boxed{\textbf{(C)}\ 36 }$

See also

2014 AMC 12B (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 12 Problems and Solutions

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