SOLUTION: There are 2 vats of orange juice. After 10% of the orange juice in the first vat is poured into the second vat, the first vat has 3 times as much orange juice as the second vat. By

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: There are 2 vats of orange juice. After 10% of the orange juice in the first vat is poured into the second vat, the first vat has 3 times as much orange juice as the second vat. By      Log On


   

Question 1007377: There are 2 vats of orange juice. After 10% of the orange juice in the first vat is poured into the second vat, the first vat has 3 times as much orange juice as the second vat. By what percent did the amount of juice in the second vat increase when the juice from the first vat was poured into it?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x amount of juice in first vat, y amount of juice in second vat, to start.


The transfer process:
0.9x in first vat;
0.10x+y in second vat;
%289%2F10%29x=3%28%281%2F10%29x%2By%29

How much change in the second vat?
3%28%281%2F10%29x%2By%29-y=%283%2F10%29x%2B3y-y=3x%2F10%2B2y

The comparison of the change to the original quantity of second vat
%283x%2F10%2B2y%29%2Fy
highight_green%283x%2F%2810y%29%2B2%29, as a fraction for the increase, and you would multiply by 100 to make this a percentage.

Any way to know the value?

Still the same amount of juice contained in the two vats as before the transfer process.
x%2By=3x%2F10%2B2y
10x%2B10y=3x%2B20y
7x=10y
x=%2810%2F7%29y
Substitute this into the fraction increase expression:


3%28%2810%2F7%29y%29%2F%2810y%29%2B2
%2830%2F7%29y%2F%2810y%29%2B2
30%2F70%2B2
3%2F7%2B2
highlight%282%263%2F7%29---------the FRACTION increase.
You can change this to percentage if you want.

The second vat increased in volume held, two and three-sevenths times.