Difference between revisions of "2005 AMC 10A Problems/Problem 5"

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[[Category:Introductory Algebra Problems]]
[[Category:Introductory Algebra Problems]]
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Revision as of 11:29, 4 July 2013


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?

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


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

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