SOLUTION: In a mixture of milk and water, their ratio is 4:5 in the first container and the same mixture has 5:1 in the second container. In what ratio should the mixture be extracted from e

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a mixture of milk and water, their ratio is 4:5 in the first container and the same mixture has 5:1 in the second container. In what ratio should the mixture be extracted from e      Log On


   

Question 1009366: In a mixture of milk and water, their ratio is 4:5 in the first container and the same mixture has 5:1 in the second container. In what ratio should the mixture be extracted from each container and poured into the third container so that the ratio of milk and water comes to 5:4 in the third container?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This might be inconsistent with the intention of the exercise, but the ratios can be changed into percents of milk.
First container, 44.44 percent
Second container, 83.33333 percent
WANTED, 55.56%

(or this could be done using ordinary fractions)

The units of measure are not given, but just assume any general units you want.
x for first container to use , y for how much of the second container;
system%28x%2By=100%2C44.44x%2B83.33y=100%2A55.56%29

44.44x%2B83.33y=5556
44.44x%2B83.33%28100-x%29=5556
44.44x%2B8333-83.33x=5556
44.44x-83.33x=5556-8333
38.89x=2777
highlight%28x=71.407%29, units to take from container 1
from the x value found,
highlight%28y=28.59%29, units to take from container 2

Find further that x%2Fy=2.5 NOT exactly, but very nearly so. This is like highlight%28highlight%28x%2Fy=5%2F2%29%29.
You could do the whole solution process using ordinary fractions, numerator denominator type, and get the same thing.