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A 19-liter mixture consists by volume of 1 part juice to 18 parts water. If x liters of juice and y  liters of water are added to this mixture to make a 54-liter mixture consisting by volume of 1 part juice to 2 parts water, what is the value of x ?

• (A) 17    CORRECT ANSWER
• (B) 18
• (C) 27
• (D) 35
• (E) 36

Explanation:

It is given that the 19-liter mixture consists by volume of 1 part juice to 18 parts water, so that there is 1 liter of juice and 18 liters of water in the mixture. Since the ratio and x liters of juice and y liters of water are added to make a mixture consisting by volume of 1 part juice to 2 parts water, then The new mixture is 54 liters; therefore, x + y = 54 - 19 = 35. The two simultaneous equations to be solved are and x + y = 35. Since the question askes for the value of x, substitute y = 35 - x into the fractional equation obtaining It follows that 2 + 2x = 18 + 35 - x or 3x = 51 so x = 17. The answer to this problem is (A).

(from the October 20, 1998 test)