A pharmacist has a 13 % alcohol solution and another 18 % alcohol solution. How much of each must he use to make 50 grams of a 14 % alcohol solution?
Answers
40 grams of 13% alcohol solution and (50 - 40) = 10grams of 18% alcohol solution.
A pharmacist has a 13 % alcohol solution and another 18 % alcohol solution.
we are to mix both alcohol solutions in such a way that mixture of 50grams contains 14% of alcohol solution.
let x gram of first solution (13% alcohol) and (50 -x) gram of 2nd solution (18% alcohol).
now, x × 13% + (50 - x) × 18% = 50 × 14%
⇒13x + 18(50 - x) = 50 × 14
⇒13x + 18 × 50 - 18x = 50 × 14
⇒-5x = 50 × 14 - 50 × 18
⇒-5x = -50 × 4
⇒x = 40
hence, 40 grams of 13% alcohol solution and (50 - 40) = 10grams of 18% alcohol solution.
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