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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...")
 
 
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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</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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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}</math> dollars total in dimes and nickels.
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-OofPirate
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==See also==
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#[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]]
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#[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]]
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#[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]]
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{{JMPSC Notice}}

Latest revision as of 16:13, 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


See also

  1. Other 2021 JMPSC Sprint Problems
  2. 2021 JMPSC Sprint Answer Key
  3. All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. JMPSC.png

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