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

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

(→‎Problem)
m (→‎Problem)
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 
==Problem==
 
==Problem==
−
A store normally sells windows at <math>100</math> 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?
+
A store normally sells windows at <math>\$100</math> 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?
  
 
<math> \textbf{(A) } 100\qquad \textbf{(B) } 200\qquad \textbf{(C) } 300\qquad \textbf{(D) } 400\qquad \textbf{(E) } 500 </math>
 
<math> \textbf{(A) } 100\qquad \textbf{(B) } 200\qquad \textbf{(C) } 300\qquad \textbf{(D) } 400\qquad \textbf{(E) } 500 </math>
Line 17: Line 17:
 
So they get <math>3-2=1</math> additional window if they purchase the windows together.  
 
So they get <math>3-2=1</math> additional window if they purchase the windows together.  
  
−
Therefore they save <math>1\cdot100=\left(\text{A}\right)100</math>.
+
Therefore they save <math>1\cdot100= \boxed{\textbf{(A) }100}</math>.
  
 
==Video Solution==
 
==Video Solution==
 
CHECK OUT Video Solution: https://youtu.be/ECBXQ1cE2SI
 
CHECK OUT Video Solution: https://youtu.be/ECBXQ1cE2SI
 +
 +
==Video Solution 2==
 +
https://youtu.be/tsai14EkXgQ
 +
 +
~Charles3829
  
 
==See also==
 
==See also==

Latest revision as of 02:42, 29 April 2023

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

See also

2005 AMC 10A (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2005_AMC_10A_Problems/Problem_5&oldid=192599"