document.write( "Question 552089: IF A TANKER TRUCK DELIVERS 1000 GALLONS OF 50 PERCENT SODIUM HYDROXIDE TO THE WATER PLANT HOW MUCH WATER DO I ADD TO GET A 25 PERCENT CONCENTRATION. \n" ); document.write( "
Algebra.Com's Answer #360097 by Theo(13342)\"\" \"About 
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let x equal number of gallons of water.
\n" ); document.write( "let y equal number of gallons of 25% sodium.
\n" ); document.write( "you get 2 formulas to work with that have to be solved simultaneously.
\n" ); document.write( "your first formula is:
\n" ); document.write( "1000 + x = y
\n" ); document.write( "this gets you total gallons of solution.
\n" ); document.write( "your second formula is:
\n" ); document.write( "1000 * .5 + x * 0 = y * .25
\n" ); document.write( "this gets you total gallon of sodium.
\n" ); document.write( "your original mixture is 50% sodium.
\n" ); document.write( "you are adding a mixture of 0% sodium.
\n" ); document.write( "your final mixture is 25% sodium.
\n" ); document.write( "your 2 equations that need to be solved simultaneously are:
\n" ); document.write( "1000 + x = y
\n" ); document.write( ".5*1000 + 0x = .25y
\n" ); document.write( "solve for y in the first equation (it's already been done).
\n" ); document.write( "substitute for y in the second equation to get:
\n" ); document.write( ".5*1000 + 0x = .25(1000+x)
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "500 = 250 + .25x
\n" ); document.write( "subtract 250 from both sides of this equation to get:
\n" ); document.write( "250 = .25x
\n" ); document.write( "divide both sides of this equation by .25 to get:
\n" ); document.write( "1000 = x which is the same as:
\n" ); document.write( "x = 1000
\n" ); document.write( "if you add 1000 gallons of water, then you will get a mixture that is 25% sodium.
\n" ); document.write( "your 2 original equations are:
\n" ); document.write( "1000 + x = y
\n" ); document.write( ".5*1000 + 0x = .25y
\n" ); document.write( "when x = 1000, your first equation becomes:
\n" ); document.write( "y = 2000
\n" ); document.write( "when x = 1000 and y = 2000, your second equation becomes:
\n" ); document.write( ".5*1000 + 0*1000 = .25*2000
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "500 = 500
\n" ); document.write( "since this equation is also true, the values of x = 1000 and y = 2000 are solutions to both equations simultaneously and are therefore valid solutions to this system of equations.
\n" ); document.write( "looked at it in another way, your original solution of 50% sodium contained 500 gallons of sodium.
\n" ); document.write( "that same 500 gallon of sodium is not part of 2000 gallons which makes it equal to 25% of the new solution. \n" ); document.write( "
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