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

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==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 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</math> dimes. |

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

+ | |||

+ | -OofPirate |

## Revision as of 01:02, 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 dimes.

The value of nickels is: , or two dollars. On the other hand, the value of dimes is: , or dollars.

Therefore, Luis has a total of dollars total in dimes and nickels.

-OofPirate