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Difference between revisions of "2021 JMPSC Sprint Problems/Problem 6"
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==Solution==
 
==Solution==
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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.  
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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.  
  
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The value of </math>40<math> nickels is: </math>40\cdot 0.05=2.00<math>, or two dollars.  
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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.
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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.
  
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Therefore, Luis has a total of </math>6+2<math> </math>=<math> </math>\boxed{8}$ dollars total in dimes and nickels.
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Therefore, Luis has a total of <math>6+2</math> <math>=</math> <math>\boxed{8}</math> dollars total in dimes and nickels.
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-OofPirate

Revision as of 00:02, 11 July 2021

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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