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. Unknown error_msg)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. Unknown error_msg)6+2$$ (Error compiling LaTeX. Unknown error_msg)=$$ (Error compiling LaTeX. Unknown error_msg)\boxed{8}$ dollars total in dimes and nickels.

Page

Toolbox

Search

2021 JMPSC Sprint Problems/Problem 6

Problem

Solution