document.write( "Question 274770: Hello I need help with this problem please.\r
\n" ); document.write( "\n" ); document.write( "Plato has 58 coins in nickels, dimes, and quarters. The number of nickels is three less than twice the number of dimes. The total value of the coins is $7.40. How many of each type of coin does Plato have? \n" ); document.write( "
Algebra.Com's Answer #200506 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
OK. We can work this problem either using one unknown or two unknowns. I will work it using one unknown and then set it up for you to solve using two unknowns.\r
\n" ); document.write( "\n" ); document.write( "Let x=number of dimes
\n" ); document.write( "Then 2x-3=number of nickels\r
\n" ); document.write( "\n" ); document.write( "Number of nickels and dimes=x+2x-3=3x-3
\n" ); document.write( "So, number of quarters=58-(3x-3)=58-3x+3=61-3x
\n" ); document.write( "Now we are told that($ understood):
\n" ); document.write( "0.10x+0.05(2x-3)+0.25(61-3x)=7.40 get rid of parens
\n" ); document.write( "0.10x+0.10x-0.15+15.25-0.75x=7.40 simplify by combining like terms
\n" ); document.write( "-0.55x+15.10=7.40 subtract 15.10 from each side
\n" ); document.write( "-0.55x+15.10-15.10=7.40-15.10 combine like terms again
\n" ); document.write( "-0.55x=-7.70 divide each side by -0.55
\n" ); document.write( "x=14--------------------number of dimes
\n" ); document.write( "2x-3=2*14-3=25----------number of nickels
\n" ); document.write( "61-3x=61-42=19-----------number of quarters
\n" ); document.write( "CK
\n" ); document.write( "14+25+19=58
\n" ); document.write( "58=58
\n" ); document.write( "and
\n" ); document.write( "0.10*14+0.05*25+0.25*19=7.40
\n" ); document.write( "1.40+1.25+4.75=7.40
\n" ); document.write( "7.40=7.40
\n" ); document.write( "Now using 2 unknowns:\r
\n" ); document.write( "\n" ); document.write( "Let x=number of dimes
\n" ); document.write( "then 2x-3=number of nickels
\n" ); document.write( "and let y=number of quarters
\n" ); document.write( "x+(2x-3)+y=58 or
\n" ); document.write( "3x-3+y=58 add three to both sides
\n" ); document.write( "3x+y=61----------------------------eq1
\n" ); document.write( "and
\n" ); document.write( "0.10x+0.05(2x-3)+0.25y=7.40 simplify
\n" ); document.write( "0.20x-0.15+0.25y=7.40 add 0.15 to each side
\n" ); document.write( "0.20x+0.25y=7.55-----------------------------eq2\r
\n" ); document.write( "\n" ); document.write( "Now just solve the two equations (hint: multiply eq2 by 4 and then subtract from eq1)\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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