document.write( "Question 1188337: Hi
\n" ); document.write( "Bottles P and Q are identical. Bottle P is 5/6 filled with water and Q is 3/4 filled with water. The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11. Their total mass is 1150g. What is the mass of one empty bottle.
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Algebra.Com's Answer #819459 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Bottles P and Q are identical.
\n" ); document.write( "Bottle P is 5/6 filled with water and Q is 3/4 filled with water.
\n" ); document.write( " The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11.
\n" ); document.write( " Their total mass is 1150g.
\n" ); document.write( " What is the mass of one empty bottle.
\n" ); document.write( ":
\n" ); document.write( "let b = the mass of one empty bottle
\n" ); document.write( "let w = the mass of the water in a full bottle
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\n" ); document.write( "\"The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11.\"
\n" ); document.write( "\"%28b%2B%285%2F6%29w%29%2F%28b%2B%283%2F4%29w%29\" = \"12%2F11\"
\n" ); document.write( "Cross multiply
\n" ); document.write( "11(b+(5/6)w) = 12(b+(3/4)w)
\n" ); document.write( "11b + (55/6)w = 12b + 3(3)w
\n" ); document.write( "11b + (55/6)w = 12b + 9w
\n" ); document.write( "Multiply by 6 get rid of the denominator
\n" ); document.write( "66b + 55w = 72b + 54w
\n" ); document.write( "55w - 54w = 72b - 66b
\n" ); document.write( "w = 6b
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\n" ); document.write( "\"Their total mass is 1150g.\"
\n" ); document.write( "2b + \"5%2F6\"w + \"3%2F4\"w = 1150
\n" ); document.write( "multiply by 12, get rid of the denominator
\n" ); document.write( "24b + 2(5)w + 3(3)w = 13800
\n" ); document.write( "24b + 10w + 9w = 13800
\n" ); document.write( "24b + 19w = 13800
\n" ); document.write( "Replace w with 6b from the 1st equation
\n" ); document.write( "24b + 19(6b) = 13800
\n" ); document.write( "24b + 114b = 13800
\n" ); document.write( "138b = 13800
\n" ); document.write( "b = 13800/138
\n" ); document.write( "b = 100 grams is the mass of the empty bottle
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\n" ); document.write( "You can check this solution by substitution in the 2nd original equation
\n" ); document.write( "w=6b
\n" ); document.write( "w=6*100
\n" ); document.write( "2(100) + (5/6)600 + (3/4)600 = \r
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