document.write( "Question 670863: I am not sure how to figure out a coin problem without how much it's worth for example: A bank contains 44 coins (nickles, dimes, quarters). There are twice as many dimes as nickles and 8 fewer nickles than quarters. How much money is in the bank? \n" ); document.write( "
Algebra.Com's Answer #417165 by Theo(13342)\"\" \"About 
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44 coins in total.
\n" ); document.write( "n = number of nickels.
\n" ); document.write( "d = number of dimes
\n" ); document.write( "q = number of quarters.
\n" ); document.write( "there are twice as many dimes as nickels.
\n" ); document.write( "d = 2n
\n" ); document.write( "8 fewer nickels than quarters.
\n" ); document.write( "n = q - 8
\n" ); document.write( "how much money is in the bank.
\n" ); document.write( "the amount of money in the bank is determined as follows:
\n" ); document.write( ".05n = amount of money in nickels.
\n" ); document.write( ".1d = amount of money in dimes.
\n" ); document.write( ".25q = amount of money in quarters.
\n" ); document.write( "you have 2 equations.
\n" ); document.write( "n + d + q = 44
\n" ); document.write( ".05n + .1d + .25q = amount of money in the bank.
\n" ); document.write( "you need to solve for n, d, and q and then you can determine how much money is in the bank.
\n" ); document.write( "start with the equation of n + d + q = 44
\n" ); document.write( "you are given that d = 2n so you can substitute 2n for d which makes the equation becomes:
\n" ); document.write( "n + 2n + q = 44
\n" ); document.write( "you are given that n = q - 8 so you can substitute q - 8 for n which makes the equation become:
\n" ); document.write( "q - 8 + 2(q - 8) + q = 44
\n" ); document.write( "since you now have 1 unknown in 1 equation, you can solve for q.
\n" ); document.write( "simplify the equation to get:
\n" ); document.write( "q - 8 + 2q - 16 + q = 44
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "4q - 24 = 44
\n" ); document.write( "add 24 to both sides of the equation to get:
\n" ); document.write( "4q = 44 + 24 = 68
\n" ); document.write( "divide both sides of the equation by 4 to get:
\n" ); document.write( "q = 68/4 = 17
\n" ); document.write( "since you know that n = q - 8, this means that n = 9
\n" ); document.write( "you have:
\n" ); document.write( "q = 17
\n" ); document.write( "n = 9
\n" ); document.write( "since you know that d = 2n, this means that d = 18
\n" ); document.write( "now you have:
\n" ); document.write( "q = 17
\n" ); document.write( "n = 9
\n" ); document.write( "d = 18
\n" ); document.write( "the first equation you had to solve is n + d + q = 44
\n" ); document.write( "replace q with 17 and n with 9 and d with 18 and you get:
\n" ); document.write( "9 + 18 + 17 = 44 which becomes 44 = 44 which is true so the numbers for n and d and q look good.
\n" ); document.write( "now to the money.
\n" ); document.write( "the equation is:
\n" ); document.write( ".05n + .1d + .25q = the money
\n" ); document.write( "replace n with 9 and d with 18 and q with 17 and you get:
\n" ); document.write( ".05(9) + .1(18) + .25(17) = .45 + 1.8 + 4.25 which is equal to 6.5 dollars that you have in the bank.\r
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