Question 726860: Please help... first time algebra student since high school 25 years ago. Thank you in advance!
A quart bottle of a drain cleaning solution is 25% sodium hydroxide (chemical formula NaOH) by weight. One quart of the solution weighs 2 lb. How many ounces of pure NaOH should be added to give a solution that is 30% NaOH by weight?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let s = the amount of sodium,lbs
Let D = the amount drain cleaner, lbs
Initially we have a quart of cleaner weighing 2 lbs. This quart is 25% sodium by weight or
(1) s = 25% of 2lbs or
(2) s = 1/4*2 or
(3) s = 1/2 lb, initially.
Now let x = the amount of sodium to add to the 2# quart of cleaner to get a 30% mixture, again all percentages are by weight.
This last statement gives us the equation
(4) (s + x)/(D + x) = 30% or
(5) (.5 + x)/(2 + x) = 0.3 or
(6) .5 + x = 0.3*(2 + x) or
(7) .5 + x = 0.6 + 0.3x or
(8) x - .3x = .6 - .5 or
(8) 0.7x = 0.1 or
(10) x = 0.1/0.7 or
(11) x = 1/7
Let's check this with (4).
Is (1/2 + 1/7)/(2 + 1/7) = 0.3)?
Is ((9/14)/(15/7) = 0.3)?
Is ((9/15)*(7/14) = 0.3)?
Is ((3/5)*(1/2) = 0.3)?
Is (3/10 = 0.3)?
Is (0.3 = 0.3)? Yes
Answer: You need to add 1/7lb of sodium hydroxide to the quart of drain cleaning solution to obtain a 30%, by weight, solution.
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