# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 6"

## 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 $60 dimes. The value of$ (Error compiling LaTeX. ! Missing $inserted.)40$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$(Error compiling LaTeX. ! Missing$ inserted.)6+2$$(Error compiling LaTeX. ! Missing  inserted.)=$$ (Error compiling LaTeX. ! Missing $inserted.)\boxed{8}$ dollars total in dimes and nickels.