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

2021 JMPSC Sprint Problems/Problem 6

Revision as of 16:13, 11 July 2021 by Samrocksnature (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Luis has $100$ coins that are all either nickels or dimes. If the probability of randomly picking a nickel from these $100$ coins is $\frac{2}{5},$ how much money does Luis have in dollars?

Solution

The probability in which a random choosing of a coin from a pool of $100$ coins bringing out a nickel is $\frac{2}{5}$. Multiplying the fraction by $\frac{20}{20}$, we get $\frac{40}{100}$, or $40$ coins out of $100$. This means that there are $40$ nickels, and $60$ dimes.

The value of $40$ nickels is: $40\cdot 0.05=2.00$, or two dollars. On the other hand, the value of $60$ dimes is: $60 \cdot 0.10=6.00$, or $6$ dollars.

Therefore, Luis has a total of $6+2$ $=$ $\boxed{8}$ dollars total in dimes and nickels.

-OofPirate


See also

  1. Other 2021 JMPSC Sprint Problems
  2. 2021 JMPSC Sprint Answer Key
  3. All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. JMPSC.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_JMPSC_Sprint_Problems/Problem_6&oldid=158027"