document.write( "Question 1156055: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85%. He wants to use all three solutions to obtain a mixture of 72 liters containing 55% acid, using 2 times as much of the 85% solution as the 40% solution. How many liters of each solution should be used? \n" ); document.write( "
Algebra.Com's Answer #778744 by Theo(13342)\"\" \"About 
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x = number of liters of 25% solution.
\n" ); document.write( "y = number of liters of 40% solution.
\n" ); document.write( "z = number of liters of 85% solution.
\n" ); document.write( "he wants 72 liters of 55% solution.
\n" ); document.write( "you have two equations that need to be solved simultaneously.
\n" ); document.write( "first is x + y + z = 72
\n" ); document.write( "second is .25 * x + .40 * y + .85 * z = .55 * 72
\n" ); document.write( "he wants to use 2 times as much of the 85% solution as the 40% solution.
\n" ); document.write( "this makes the third equation be z = 2 * y
\n" ); document.write( "you now have three equations that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "first equation is x + y + z = 72
\n" ); document.write( "second equation is .25 * x + .40 * y + .85 * z = .55 * 72
\n" ); document.write( "third equation is z = 2 * y
\n" ); document.write( "use the third equation to replace z with 2 * y in the first two equations.
\n" ); document.write( "first two equations becomes:
\n" ); document.write( "x + y + 2 * y = 72
\n" ); document.write( ".25 * x + .40 * y + .85 * 2 * y = .55 * 72
\n" ); document.write( "simplify and combine like terms to get:
\n" ); document.write( "x + 3 * y = 72
\n" ); document.write( ".25 * x + 2.1 * y = 39.6
\n" ); document.write( "multiply both sides of the first equation by .25 and leave the second equation as is to get:
\n" ); document.write( ".25 * x + .25 * 3 * y = .25 * 72
\n" ); document.write( ".25 * x + 2.1 * y = 39.6
\n" ); document.write( "simplify to get:
\n" ); document.write( ".25 * x + .75 * y = 18
\n" ); document.write( ".25 * x + 2.1 * y = 39.6
\n" ); document.write( "subtract the first equation from the second to get:
\n" ); document.write( "1.35 * y = 21.6
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 21.6 / 1.35 = 16
\n" ); document.write( "since z = 2 * y, then z = 32
\n" ); document.write( "since x + y + z = 72, then x = 72 - 32 - 16 = 24
\n" ); document.write( "you now have:
\n" ); document.write( "x = 24
\n" ); document.write( "y = 16
\n" ); document.write( "z = 32
\n" ); document.write( "first original is true because they all add up to 72.
\n" ); document.write( "second original equation is:
\n" ); document.write( ".25 * x + .40 * y + .85 * z = .55 * 72
\n" ); document.write( "it becomes:
\n" ); document.write( ".25 * 24 + .40 * 16 + .85 * 32 = .55 * 72
\n" ); document.write( "simplify to get:
\n" ); document.write( "6 + 6.4 + 27.2 = 39.6
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "39.6 = 39.6
\n" ); document.write( "this confirms the values of x, y, and z are good.
\n" ); document.write( "your solution is:
\n" ); document.write( "24 liters of 25% solution and 16 liters of 40% and 32 liters of 85% will give you 72 liters of 55% solution.
\n" ); document.write( "to confirm, do the following:
\n" ); document.write( "24 * .25 + 16 * .40 + 32 * .85 = 39.6
\n" ); document.write( "39.6 / 72 = .55 = 55%.\r
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