Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

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

(added problem and solution)
 
m (added category)
Line 25: Line 25:
  
 
*[[2005 AMC 10A Problems/Problem 6|Next Problem]]
 
*[[2005 AMC 10A Problems/Problem 6|Next Problem]]
 +
 +
[[Category:Introductory Algebra Problems]]

Revision as of 20:44, 3 August 2006

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2005_AMC_10A_Problems/Problem_5&oldid=9204"