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

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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\times2  \implies \boxed{\textbf{(C)}\ 36 }</math>
 
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\times2  \implies \boxed{\textbf{(C)}\ 36 }</math>
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{{AMC12 box|year=2014|ab=B|num-b=1|num-a=3}}
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{{MAA Notice}}

Revision as of 13:05, 21 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. ! Extra }, or forgotten $.)

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

2014 AMC 12B (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 12 Problems and Solutions

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