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

Revision as of 18:07, 25 December 2022

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?

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

Solution

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

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

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

This is a total of $2$ free windows.

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

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

Therefore they save $1\cdot100= \boxed{\textbf{(A) }100}$ .

Video Solution

CHECK OUT Video Solution: https://youtu.be/ECBXQ1cE2SI

Video Solution 2

https://youtu.be/tsai14EkXgQ

~Charles3829

2005 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AMC 10 Problems and Solutions

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

@@ Line 21: / Line 21: @@
 ==Video Solution==
 CHECK OUT Video Solution: https://youtu.be/ECBXQ1cE2SI
+==Video Solution 2==
+https://youtu.be/tsai14EkXgQ
+~Charles3829
 ==See also==

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