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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Revision as of 13:05, 21 February 2014
Problem
Orvin went to the store with just enough money to buy balloons. When he arrived he discovered that the store had a special sale on balloons: buy balloon at the regular price and get a second at 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 dollars, then Orvin has dollars. For every balloon he buys for dollars, he can buy another for dollars. This means it costs him dollars to buy a bundle of balloons. With dollars, he can buy sets of two balloons, so the total number of balloons he can buy is
2014 AMC 12B (Problems • Answer Key • Resources) | |
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Followed by Problem 3 |
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