A chemist has 80 pints of a 20% iodine solution. How many pints of iodine must be added to produce a solution that is 33.1/3% iodine?
Please help me work this through
Let X be the number of pints of iodine that must be added.
You start out with a mix that contains 16 pints of pure iodine and 64 of solvent. You keep the amount of solvent the same and add X pints of iodine. The new fraction of iodine is
(16 + X)/(80 + X) = 1/3
16 + X = 80/3 + X/3
(2X/3) = 32/3
X = ?
To solve for X, let's first simplify the equation:
(2X/3) = 32/3
Next, we'll cross multiply:
3 * 32 = 2X * 3
96 = 6X
Finally, divide both sides of the equation by 6:
96/6 = X
X = 16
Therefore, 16 pints of iodine must be added to produce a solution that is 33 1/3% iodine.