document.write( "Question 1102980: Emma Hodges has a jar containing 65 coins, all of which are either nickels or dimes. The total value of the cons is $5.30. How many of each does she have? \n" ); document.write( "
Algebra.Com's Answer #717685 by Theo(13342)![]() ![]() You can put this solution on YOUR website! n = number of nickels. \n" ); document.write( "d = number of dimes.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "first equation is n + d = 65\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "a nickel is worth 5 cents. \n" ); document.write( "a dime is worth 10 cents. \n" ); document.write( "5 dollars and thirty cents is worth 530 cents.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "second equation is 5n + 10d = 530\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you have 2 equations that need to be solved simultaneously.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "they are:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "n + d = 65 \n" ); document.write( "5n + 10d = 530\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "from the first equation, solve for n to get n = 65 -d.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "in the second equation, replace n with 65 - d to get 5 * (65 - d) + 10d = 530. \n" ); document.write( "simplify to get 325 - 5d + 10d = 530 \n" ); document.write( "combine like terms to get 325 + 5d = 530 \n" ); document.write( "subtract 325 from both sides of this equation to get 5d = 205 \n" ); document.write( "solve for d to get d = 205/5 = 41\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since n + d = 65, n must be equal to 24 because 41 + 24 = 65.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you have:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "n = 24 \n" ); document.write( "d = 41\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "n + d = 65 \n" ); document.write( "5n + 10d = 5*24 + 10*41 = 120 + 410 = 530\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solution looks good.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solution is she has 24 nickels and 41 dimes in the jar.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |