Rastis wrote:Can someone provide a way to decipher these type of mixing questions? I always have an extremely hard time even setting this problem up. Also Mitch, can you better explain your "alligation"? It's very hard to interpret what you're trying to say.
To illustrate:
X = 10% alcohol
Y = 30% alcohol
Z = percentage of alcohol in a mixture of X and Y
Alligation uses the RELATIVE DISTANCES to determine the proportion needed of X and Y.
If Z is EQUIDISTANT from X and Y, EQUAL amounts of X and Y are needed.
If Z = 20% -- HALFWAY between X and Y -- EQUAL amounts of X and Y will yield the desired percentage.
In other words, X:Y = 1:1.
If we mix 100 liters of X and 100 liters of Y, the percentage of alcohol in Z = alcohol/total = (10+30)/200 = 1/5 = 20%.
The CLOSER Z gets to Y, the MORE we need of Y, the LESS we need of X.
If Z = 25%, which is CLOSER to Y:
The distance between Z and Y tells us the proportion needed of X: 30-25 = 5.
The distance between Z and X tells us the proportion needed of Y: 25-10 = 15.
X:Y = 5:15 = 1:3.
Since the desired percentage is CLOSER to Y, we need LESS of X and MORE of Y.
To confirm that the ratio is correct:
If we mix 100 liters of X and 300 liters of Y, the percentage of alcohol in Z = alcohol/total = (10 + 3*30)/400 = 1/4 = 25%.
The CLOSER Z gets to X, the MORE we need of X, the LESS we need of Y.
If Z = 15%, which is closer to X:
The distance between Z and Y tells us the proportion needed of X: 30-15 = 15.
The distance between Z and X tells us the proportion needed of Y: 15-10 =5.
X:Y = 15:5 = 3:1.
Since the desired percentage is CLOSER to X, we need MORE of X and LESS of Y.
To confirm that the ratio is correct:
If we mix 300 liters of X and 100 liters of Y, the percentage of alcohol in Z = alcohol/total = (3*10 + 30)/400 = 3/20 = 15%.
With this explanation in mind, please revisit my solution above.
Here are some other alligation problems:
https://www.beatthegmat.com/allegation-t69552.html
https://www.beatthegmat.com/mixture-prob ... 89508.html
https://www.beatthegmat.com/mixture-with ... 82022.html
https://www.beatthegmat.com/problem-from ... 49413.html
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