zaarathelab wrote:Solution X contains only ingredients A and B in a ratio of 2:3. Solution Y contains only ingredients A and B in the ratio 1:2. If solution Z is created by mixing solutions X and Y in the ratio of 3:11, then 630 ounces of solution Z contains how many ounces of a?
a) 68
b) 73
c) 89
d) 219
e) 236
Pls give the shortest way to do this.
Solution Z: 630 ounces
X:Y = 3:11.
This means that of every 14 ounces, 3 ounces are X and 11 ounces are Y.
In other words, X is 3/14 of the total:
X = (3/14)630 = 135 ounces.
Y = 630-135 = 495 ounces.
Solution X: 135 ounces
A:B = 2:3.
This means that of every 5 ounces, 2 ounces are A and 3 ounces are B.
In other words, A is 2/5 of the total:
A = (2/5)135 = 54 ounces.
Solution Y: 495 ounces
A:B = 1:2.
This means that of every 3 ounces, 1 ounce is A and 2 ounces are B.
In other words, A is 1/3 of the total:
A = (1/3)495 = 165 ounces.
Total amount of A = 54+165 = 219 ounces.
The correct answer is
D.
Fastest approach:
In the mixture, Y:X = 11:3.
The relative amount of Y (11) is almost 4 times the relative amount of X (3).
Since most of the mixture will come from Y, the fraction of A in the mixture will be very close to the fraction of A in Y:
(1/3)630 = 210.
Since about 1/5 of the mixture will come from X -- and X contains a slightly higher percentage of A -- the actual amount of A in the mixture will be just a bit more than 210.
The correct answer is
D.
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