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2021 JMPSC Sprint Problems/Problem 6

Revision as of 00:02, 11 July 2021 by Oofpirate (talk | contribs)

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

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