document.write( "Question 1046531: How do you set up this problem for solving? Steve is cashing in his jar of spare nickels dimes and quarters. When he gets to the bank he receives a total of $14.70. He learned he had 133 coins in all, and that there were 3 times as many dimes as quarters. How many of each type of each type of coin did he save? \n" ); document.write( "
Algebra.Com's Answer #661962 by ikleyn(52874)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "How do you set up this problem for solving? Steve is cashing in his jar of spare nickels dimes and quarters.
\n" ); document.write( "When he gets to the bank he receives a total of $14.70.
\n" ); document.write( "He learned he had 133 coins in all, and that there were 3 times as many dimes as quarters.
\n" ); document.write( "How many of each type of each type of coin did he save?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let n = # of nickels, d = # of dimes, q = # of quarters.\r\n" );
document.write( "\r\n" );
document.write( "Then immediately from the condition you have these system of three equations for three unknowns:\r\n" );
document.write( "\r\n" );
document.write( " n +   d +   q =  133,       (1)      (\"he had 133 coins in all\")\r\n" );
document.write( "5n + 10d + 25q = 1470,       (2)      (\"When he gets to the bank he receives a total of $14.70\")\r\n" );
document.write( "d = 3q.                      (3)\r\n" );
document.write( "\r\n" );
document.write( "Next, we reduce this 3x3 system to the more simple 2x2 system of two equations for two unknowns:\r\n" );
document.write( "\r\n" );
document.write( "For it, I substitute (replace) \"d\" in equations (1) and (2) by 3q based on equation (3). I will get\r\n" );
document.write( "\r\n" );
document.write( " n +     3q  +   q =  133,   (4)\r\n" );
document.write( "5n + 10*(3q) + 25q = 1470.   (5)\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( " n +  4q =  133,             (6)\r\n" );
document.write( "5n + 55q = 1470.             (7)\r\n" );
document.write( "\r\n" );
document.write( "OK. So, you have now much simpler system (6), (7). To solve it, express n = 133-4q  from (6) and substitute it into (7). You will get\r\n" );
document.write( "\r\n" );
document.write( "5*(133-4q) + 55q = 1470,  or\r\n" );
document.write( "\r\n" );
document.write( "665 - 20q + 55q = 1470  --->  35q = 1470 - 665  --->  35q = 805  --->  q = \"805%2F35\" = 23.\r\n" );
document.write( "\r\n" );
document.write( "So we just found the number of quarters. It is 23. There were 23 quarters.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of dimes is trice of it: there were 3*23 = 69 dimes.\r\n" );
document.write( "\r\n" );
document.write( "Now the number of nickels is simply 133 - 69 - 23 = 41.\r\n" );
document.write( "\r\n" );
document.write( "Check.  5*41 + 10*69 + 23*25 = 1470.  Correct!\r\n" );
document.write( "\r\n" );
document.write( "Answer.  41 nickels, 69 dimes and 23 quarters.\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Please ignore what the other tutor, \"josgarithmetic\" wrote in his post.
\n" ); document.write( "He is not able to solve word problems correctly, as well to explain the solutions.
\n" ); document.write( "I don't know what he is doing in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Regarding the coin problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - More Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Kevin and Randy Muise have a jar containing coins\r
\n" ); document.write( "\n" ); document.write( "    - Typical coin problems from the archive
\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );