# Math Multiple Choice

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 + 2*x* = 18 + 35 - *x* or 3*x* = 51 so *x* = 17. The answer to this problem is (A).

(from the October 20, 1998 test)