Rudy414 wrote:The afternoon after a party, Traci prepares a cleaning solution of x liters of water and y liters of bleach. The bleach comes in half-liter containers. How many such containers will Traci require for her cleaning solution?
1) Traci will need a total of 25 liters of solution altogether.
2) To halve the concentration of bleach in her solution, Traci would need to add 2.4y liters of water, and reduce the number of liters of bleach by 1.
We need to determine the value of 2y, i.e. the value of y.
Statement 1: (x + y) = 25
As we don't know x, we cannot determine y.
Not sufficient
Statement 2: Original concentration of bleach = y/(x + y)
New concentration of bleach = (y - 1)/[(x + 2.4y) + (y - 1)]
So, (y - 1)/[(x + 2.4y) + (y - 1)] = [y/(x + y)]/2
--> 2(y - 1)/(x + 3.4y - 1) = y/(x + y)
--> 2(y - 1)(x + y) = y(x + 3.4y - 1)
This will give us a quadratic equation in y with x as the coefficient. As we don't know x, we cannot determine y.
Not sufficient
1 & 2 Together: From statement 1 --> (x + y) = 25
And from statement 2,
--> 2(y - 1)(x + y) = y(x + 3.4y - 1)
--> 2(y - 1)(x + y) = y(2.4y + x + y - 1)
--> 50(y - 1) = y(2.4y + 24)
--> 2.4y² - 26y + 50 = 0
--> 12y² - 130y + 250 = 0
--> 6y² - 65y + 125 = 0
--> 6y² - 15y - 50y + 125 = 0
--> 3y(2y - 5) - 25(2y - 5) = 0
--> (2y - 5)(3y - 25) = 0
Hence, y can be 5/2 or 25/3
Not sufficient
The correct answer is E.
