document.write( "Question 1100355: Sam has $3.15 in quarters nickels and dimes he has half as many quarters as he has dimes and nickels together he also has two more nickels than dimes how many of each coin are there \n" ); document.write( "
Algebra.Com's Answer #846475 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "In fact, you can even use artificial intelligence.  You cannot trust AI for\r\n" );
document.write( "advanced stuff, but it can solve simple stuff very easily.  I copied and pasted\r\n" );
document.write( "exactly word-for word what you posted above (without punctuation marks) into: \r\n" );
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document.write( "https://poe.com/\r\n" );
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document.write( "and here's what I got (copied and pasted) from that site:\r\n" );
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document.write( "Let's define the variables for the coins:\r\n" );
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document.write( "Let 𝑑 be the number of dimes.\r\n" );
document.write( "Let 𝑛 be the number of nickels.\r\n" );
document.write( "Let 𝑞 be the number of quarters.\r\n" );
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document.write( "From the problem, we have the following relationships:\r\n" );
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document.write( "The total value of the coins is $3.15, which is 315 cents:\r\n" );
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document.write( "10𝑑+5𝑛+25𝑞=315\r\n" );
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document.write( "Sam has half as many quarters as the total number of dimes and nickels:\r\n" );
document.write( "𝑞=1/2(𝑑+𝑛)\r\n" );
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document.write( "He has two more nickels than dimes:\r\n" );
document.write( "𝑛=𝑑+2\r\n" );
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document.write( "Now, we can substitute 𝑛 in terms of 𝑑 into the other equations. \r\n" );
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document.write( "From the third equation, we have: 𝑛=𝑑+2\r\n" );
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document.write( "Substituting 𝑛 into the second equation:\r\n" );
document.write( "𝑞=(1/2)(𝑑+(𝑑+2))=(1/2)(2d+2)=d+1\r\n" );
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document.write( "Now substituting 𝑛 and 𝑞 into the first equation:\r\n" );
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document.write( "10𝑑+5(𝑑+2)+25(𝑑+1)=315\r\n" );
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document.write( "Expanding this gives:\r\n" );
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document.write( "10𝑑+5𝑑+10+25𝑑+25=315\r\n" );
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document.write( "40𝑑+35=315\r\n" );
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document.write( "Now, subtract 35 from both sides:\r\n" );
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document.write( "40𝑑=280\r\n" );
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document.write( "Dividing by 40:\r\n" );
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document.write( "𝑑=7\r\n" );
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document.write( "Now that we have d, we can find 𝑛 and 𝑞\r\n" );
document.write( "𝑛=𝑑+2=7+2=9\r\n" );
document.write( "𝑞=𝑑+1=7+1=8\r\n" );
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document.write( "Thus, the solution is:\r\n" );
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document.write( "Dimes (d): 7\r\n" );
document.write( "Nickels (𝑛): 9\r\n" );
document.write( "Quarters (𝑞): 8\r\n" );
document.write( "Final Answer:\r\n" );
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document.write( "Dimes: 7\r\n" );
document.write( "Nickels: 9\r\n" );
document.write( "Quarters: 8\r\n" );
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document.write( "That was all copied and pasted exactly as poe.com printed instantly. But\r\n" );
document.write( "don't depend on it for more advanced math.  It will sometimes make stupid\r\n" );
document.write( "mistakes.  AI is not perfected yet.  But someday it will be, and will take us\r\n" );
document.write( "all over, just as Stephen Hawking warned. LOL (Maybe I shouldn't be laughing).\r\n" );
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document.write( "Edwin
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