document.write( "Question 1154912: You have $144 in one-, five-, and ten-dollar bills. There are 35 bills in total, and two more ten-dollar bills than five-dollar bills. How many bills of each type are there? \n" ); document.write( "
Algebra.Com's Answer #777441 by Theo(13342)\"\" \"About 
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let x = the number of 1 dollar bills and y = the number of 5 dollar bills and z = the number of 10 dollar bills.
\n" ); document.write( "you get:
\n" ); document.write( "x + y + z = 35
\n" ); document.write( "x + 5y + 10z = 144
\n" ); document.write( "since you have 2 more 10 dollar bills than 5 dollar bills, you get:
\n" ); document.write( "z = y + 2
\n" ); document.write( "replace z with y + 2 in the first 2 equations to get:
\n" ); document.write( "x + y + y + 2 = 35
\n" ); document.write( "x + 5y + 10 * (y + 2) = 144
\n" ); document.write( "simplify both equations to get:
\n" ); document.write( "x + 2y + 2 = 33
\n" ); document.write( "x + 5y + 10y + 20 = 144
\n" ); document.write( "subtract the constants on the left side of the equation from both sides of the equation and simplify further to get:
\n" ); document.write( "x + 2y = 33
\n" ); document.write( "x + 15y = 124
\n" ); document.write( "subtract the first equation from the first to get:
\n" ); document.write( "13y = 91
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 91 / 13 = 7
\n" ); document.write( "since z = y + 2, then z = 9
\n" ); document.write( "first original equation becomes:
\n" ); document.write( "x + 7 + 9 = 35
\n" ); document.write( "solve for x to get x = 35 - 16 = 19
\n" ); document.write( "you have:
\n" ); document.write( "x = 19
\n" ); document.write( "y = 7
\n" ); document.write( "z = 9
\n" ); document.write( "second original equation becomes:
\n" ); document.write( "19 * 1 + 7 * 5 + 9 * 10 = 19 + 35 + 90 = 144
\n" ); document.write( "both original equations are true when x = 19 and y = 7 and z = 9
\n" ); document.write( "you have 19 one dollar bills and 7 five dollar bills and 9 ten dollar bills.
\n" ); document.write( "that's your solution.\r
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