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.

2012 CEMC Gauss (Grade 8) Problems/Problem 5

Revision as of 15:33, 20 April 2025 by Anabel.disher (talk | contribs) (Undo revision 247023 by Anabel.disher (talk))

Problem

How many more coins does it take to make one dollar (100) using only nickels(5 coins) than it takes to make one dollar using only dimes(10 coins)?

$\text{ (A) }\ 15\qquad\text{ (B) }\ 10\qquad\text{ (C) }\ 75\qquad\text{ (D) }\ 64\qquad\text{ (E) }\ 54$

Solution

Since a dollar is $100$ cents and a nickel is $5$ cents, there are $\frac{100}{5} = 20$ nickels in a dollar.

Using this logic for dimes and the fact that a dime is $10$ cents, there are $\frac{100}{10} = 10$ dimes in a dollar.

Thus, it takes $20 - 10 = \boxed{\textbf{(B) } 10}$ more coins to make a dollar using only nickels than it takes to make one dollar using only dimes.

~anabel.disher

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2012_CEMC_Gauss_(Grade_8)_Problems/Problem_5&oldid=247024"