Bunuel
A solution that is 40% acid must be strengthened to become a solution that is 88% acid. If there are 10 ounces of the 40% solution, how much pure acid must be added?
A. 2.5 ounces
B. 18 ounces
C. 28 ounces
D. 40 ounces
E. 48 ounces
I'd test the answer choices (possibly with a bit of estimation) on this one. The answer choices are easy numbers, while the math will require some algebra, so let's make it easier on ourselves.
Initially, we have 10 ounces of the solution, and .4(10) = 4 ounces of that consists of acid.
Start by testing (B): if we add 18 ounces of acid, we now have a total of 10+18 = 28 ounces of solution, and 4 + 18 = 22 ounces of that is acid.
How does 22/28 compare to 88%? It looks like we need an easy way to compare 88% to a bunch of different fractions, so let's convert 88% to a fraction as well: 88% = 88/100 = 22/25.
22/28 has a bigger denominator than 22/25, and the same numerator. Therefore, 22/28 is
too small and we need to test a bigger answer choice.
Next, test (D): if we add 40 ounces of acid, we have a total of 10 + 40 = 50 ounces of solution, and 4 + 40 = 44 ounces of that is acid.
44/50 = 88/100 = 88%.
The correct answer is (D).