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Revision as of 10:29, 4 July 2013

Problem

A store normally sells windows at $100$ each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?

$\mathrm{(A) \ } 100\qquad \mathrm{(B) \ } 200\qquad \mathrm{(C) \ } 300\qquad \mathrm{(D) \ } 400\qquad \mathrm{(E) \ } 500$

Solution

The store's offer means that every $5$th window is free.

Dave would get $\lfloor\frac{7}{5}\rfloor=1$ free window.

Doug would get $\lfloor\frac{8}{5}\rfloor=1$ free window.

This is a total of $2$ free windows.

Together, they would get $\lfloor\frac{8+7}{5}\rfloor = \lfloor\frac{15}{5}\rfloor=3$ free windows.

So they get $3-2=1$ additional window if they purchase the windows together.

Therefore they save $1\cdot100=100\Rightarrow A$

See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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