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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal number of gallons of water.
let y equal number of gallons of 25% sodium.
you get 2 formulas to work with that have to be solved simultaneously.
your first formula is:
1000 + x = y
this gets you total gallons of solution.
your second formula is:
1000 * .5 + x * 0 = y * .25
this gets you total gallon of sodium.
your original mixture is 50% sodium.
you are adding a mixture of 0% sodium.
your final mixture is 25% sodium.
your 2 equations that need to be solved simultaneously are:
1000 + x = y
.5*1000 + 0x = .25y
solve for y in the first equation (it's already been done).
substitute for y in the second equation to get:
.5*1000 + 0x = .25(1000+x)
simplify this equation to get:
500 = 250 + .25x
subtract 250 from both sides of this equation to get:
250 = .25x
divide both sides of this equation by .25 to get:
1000 = x which is the same as:
x = 1000
if you add 1000 gallons of water, then you will get a mixture that is 25% sodium.
your 2 original equations are:
1000 + x = y
.5*1000 + 0x = .25y
when x = 1000, your first equation becomes:
y = 2000
when x = 1000 and y = 2000, your second equation becomes:
.5*1000 + 0*1000 = .25*2000
simplify this equation to get:
500 = 500
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.
looked at it in another way, your original solution of 50% sodium contained 500 gallons of sodium.
that same 500 gallon of sodium is not part of 2000 gallons which makes it equal to 25% of the new solution.
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