document.write( "Question 1147868: Suppose you have just enough money, in coins, to pay for a loaf of bread priced at $1.95. You have 12 coins, all quarters and dimes. Let q equal the number of quarters and d equal the number of dimes. How many of each coin do you have? \r
\n" ); document.write( "\n" ); document.write( "I have the answer as 5 quarters and 7 dimes. I got it just by using common sense and did it in my head. Though, I would like to know how to actually solve it. All i’m really looking for is for the equation/s. From there on, I can figure out if it is substitution or elimination and solve it myself. \n" ); document.write( "
Algebra.Com's Answer #769218 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The important part of your question is about setting up the equations. You have two pieces of information:
\n" ); document.write( "(1) the total number of coins (quarters and dimes) is 12
\n" ); document.write( "(2) the value of the coins -- 25 cents for each quarter and 10 cents for each dime -- is $1.95, or 195 cents

\n" ); document.write( "If you (logically) use q for the number of quarters and d for the number of dimes, then

\n" ); document.write( "(1) the given number of coins is the sum of the number of quarters and the number of dimes:
\n" ); document.write( "\"12+=+q%2Bd\"
\n" ); document.write( "(2) the value (in cents) of q quarters is 25*q or 25q; the value of d dimes is 10*d or 10d; the given total value of the coins is the sum of the values of the quarters and dimes:
\n" ); document.write( "\"195+=+25q%2B10d\"

\n" ); document.write( "Those are the equations shown by the other tutor, though not in exactly the same form.

\n" ); document.write( "You said you knew you could figure out, once you saw the equations, \"...if it is substitution or elimination...\". Note of course that you can always use either method.

\n" ); document.write( "The other tutor showed a solution using substitution, which would not be my choice. Whenever the two equations are in this form, I find elimination far easier; there is no need to solve for one variable and substitute.
\r\n" );
document.write( "\r\n" );
document.write( "    25q + 10d = 195\r\n" );
document.write( "      q +   d = 12\r\n" );
document.write( "\r\n" );
document.write( "Multiply the the second equation by 10 and subtract from the first:\r\n" );
document.write( "\r\n" );
document.write( "    25q + 10d = 195\r\n" );
document.write( "    10q + 10d = 120\r\n" );
document.write( "   -----------------\r\n" );
document.write( "    15q       = 75\r\n" );
document.write( "\r\n" );
document.write( "Then\r\n" );
document.write( "\r\n" );
document.write( "   q = 75/15 = 5\r\n" );
document.write( "   d = 12-q = 7

\n" ); document.write( "But, again, the choice of method is yours.... \n" ); document.write( "
\n" );