document.write( "Question 115263: Painting:\r
\n" ); document.write( "\n" ); document.write( "A painter wishes to mix paint worth $15 per gallon with paint worth $18 per gallon to make a 12 gallon mixture worth $16.75 per gallon. How many gallons of each should he mix? \n" ); document.write( "

Algebra.Com's Answer #83893 by ganesh(20) $\"\"$ $\"About$

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Let x gallons of $15 paint and y gallons of $18 paint are mixed to get 12 gallons of $16.75 paint.\r
\n" ); document.write( "\n" ); document.write( "From this, we come to know, x + y = 12. \r
\n" ); document.write( "\n" ); document.write( "Also, the rate of 12 gallons mixture paint = 12 * 16.75 = $201.\r
\n" ); document.write( "\n" ); document.write( "This should be equal to 15x + 18y.\r
\n" ); document.write( "\n" ); document.write( "So, we get 15x + 18y = 201 -----------(1)\r
\n" ); document.write( "\n" ); document.write( "We already have x + y = 12 -----------(2)\r
\n" ); document.write( "\n" ); document.write( "(2)* 15 gives, 15x + 15y = 180 -------(3)\r
\n" ); document.write( "\n" ); document.write( "(1) - (3) gives, 3y = 21.\r
\n" ); document.write( "\n" ); document.write( "This gives, y = 7.\r
\n" ); document.write( "\n" ); document.write( "Plug in (2). We get, x = 5.\r
\n" ); document.write( "\n" ); document.write( "So, 5 gallons of $15 paint and 7 gallons of $18 paint gives a mixture of 12 gallons of $16.75 paint. \n" ); document.write( "

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