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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

Dr. Jekyll has discovered 'substance H', an ingredient that can turn him into Mr. Hyde. He needs, however, to produce a potion that has a concentration of 40% of substance H. Through his process of distillation, he can only obtain an aqueous solution that has a concentration of 68% of substance H. How much water must he add in order to dilute it down to 40%?

(characters from R. L. Stevenson's "The Strange Case of Dr. Jekyll and Mr. Hyde")

Assume he makes 100 mL of potion. There are 68 mL of pure substance H in this quantity. The rest, 32 mL is water.

We must add x mL of water to get a concentration of 45%:

equation

Solving for x:

equation

equation

equation

equation

We must add 70 mL of water.