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

(Created page with "==Problem== Luis has <math>100</math> coins that are all either nickels or dimes. If the probability of randomly picking a nickel from these <math>100</math> coins is <math>\f...") |
|||

Line 3: | Line 3: | ||

==Solution== | ==Solution== | ||

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

+ | |||

+ | The value of </math>40<math> nickels is: </math>40\cdot 0.05=2.00<math>, or two dollars. | ||

+ | On the other hand, the value of </math>60<math> dimes is: </math>60 \cdot 0.10=6.00<math>, or </math>6<math> dollars. | ||

+ | |||

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

## Revision as of 01:00, 11 July 2021

## Problem

Luis has coins that are all either nickels or dimes. If the probability of randomly picking a nickel from these coins is how much money does Luis have in dollars?

## Solution

The probability in which a random choosing of a coin from a pool of coins bringing out a nickel is . Multiplying the fraction by , we get , or coins out of . This means that there are nickels, and $60 dimes.

The value of$ (Error compiling LaTeX. ! Missing $ inserted.)4040\cdot 0.05=2.006060 \cdot 0.10=6.006$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.