document.write( "Question 201379: A coin bank contains 25 coins in nickles, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is $2.05. How many dimes are in the bank? \n" ); document.write( "
Algebra.Com's Answer #151636 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
Let x=number of quarters
\n" ); document.write( "Then 4x =number of dimes
\n" ); document.write( "And y=number of nickels
\n" ); document.write( "Now we are told that:\r
\n" ); document.write( "\n" ); document.write( "x+4x+y=25 or
\n" ); document.write( "5x+y=25--------------------eq1
\n" ); document.write( "also (we'll deal in pennies)
\n" ); document.write( "25x+10*4x+5y=205
\n" ); document.write( "65x+5y=205-------------------------eq2
\n" ); document.write( "multiply eq1 by 5 and then subtract it from eq2
\n" ); document.write( "(65x+5y=205)-(25x+5y=125) and we get
\n" ); document.write( "40x=80
\n" ); document.write( "x=2---------------number of quarters
\n" ); document.write( "4x=4*2=8 number of dimes
\n" ); document.write( "There must be 25-10=15 nickels\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "2*25+8*10+15*5=205
\n" ); document.write( "50+80+75=205
\n" ); document.write( "205=205\r
\n" ); document.write( "\n" ); document.write( "We can also work this problem using only one unknown:
\n" ); document.write( "Let x=number of quarters
\n" ); document.write( "Then 4x =number of dimes
\n" ); document.write( "And 25-5x=number of nickels
\n" ); document.write( "So we have:
\n" ); document.write( "25x+10*4x+5(25-5x)=205 get rid of parens
\n" ); document.write( "25x+40x+125-25x=205 subtract 125 from each side
\n" ); document.write( "25x+40x+125-125-25x=205-125 collect like terms
\n" ); document.write( "40x=80---same as before\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );