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 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}$ dollars total in dimes and nickels.

Revision as of 01:00, 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$ (Error compiling LaTeX. ! Missing $ inserted.)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. ! Missing $ inserted.)6+2$$ (Error compiling LaTeX. ! Missing $ inserted.)=$$ (Error compiling LaTeX. ! Missing $ inserted.)\boxed{8}$ dollars total in dimes and nickels.

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