document.write( "Question 128861This question is from textbook Introductory Algebra
\n" );
document.write( ": I need help with this word problem. Thanks in advance!\r
\n" );
document.write( "\n" );
document.write( "A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz. mixture that is two-thirds pure gold?
\n" );
document.write( "I have come up with:
\n" );
document.write( "First + Second = Mixture
\n" );
document.write( "x + y = 6 oz
\n" );
document.write( "3/4 + 5/12 = 2/3
\n" );
document.write( "3/4x + 5/12y = ?4 \n" );
document.write( "
Algebra.Com's Answer #94253 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz. mixture that is two-thirds pure gold? \n" ); document.write( "I have come up with: \n" ); document.write( "First + Second = Mixture \n" ); document.write( "Let \"x\" be amount of (3/4) gold ; Let \"y\" be amount of (5/12) gold. \n" ); document.write( "EQUATIONS: \n" ); document.write( "Weight Equation: x + y = 6 oz \n" ); document.write( "Gold Equation: (3/4)x + (5/12)y = (2/3)6 = 4 oz\r \n" ); document.write( "\n" ); document.write( "------------------------ \n" ); document.write( "Rearrange: \n" ); document.write( "x = 6-y \n" ); document.write( "-------- \n" ); document.write( "Substitute to solve for y: \n" ); document.write( "(3/4)(6-y) + (5/12)y = 4 \n" ); document.write( "Multiply thru by 12 to get: \n" ); document.write( "9(6-y) + 5y = 48 \n" ); document.write( "54-9y + 5y = 48 \n" ); document.write( "-4y = -6 \n" ); document.write( "y = 3/2 (amount of 5/12 gold) \n" ); document.write( "------------ \n" ); document.write( "Substitute into x = 6-y to solve for \"x\": \n" ); document.write( "x = 6-(3/2)= 9/2 (amount of 3/4 gold) \n" ); document.write( "=================== \n" ); document.write( "Cheers, \n" ); document.write( "Stan H.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |