SOLUTION: The ratio of milk:water in two vessels is 4:3 and 9:1 respectively. what ratio of contents of the two vessels should be mixed so that ratio of milk:water in resulting mixture is 3:

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of milk:water in two vessels is 4:3 and 9:1 respectively. what ratio of contents of the two vessels should be mixed so that ratio of milk:water in resulting mixture is 3:      Log On


   

Question 793779: The ratio of milk:water in two vessels is 4:3 and 9:1 respectively. what ratio of contents of the two vessels should be mixed so that ratio of milk:water in resulting mixture is 3:2?
Options: a)13:3 b)21:2 c)19:7 d)11:2
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Best to view this as a mixture problem and focus on the concentration of milk in the two vessels. Do as normal fractions if this is most comfortable.
vessel, 4/7 milk.
vessel other, 9/10 milk.
Want 3/5 milk.

We do not yet know how much from the 4/7 vessel nor from the 9/10 vessel, but we can assume any number of parts total in the final mixture.

Try this:
x parts of the 4/7 milk
y parts of the 9/10 milk
x%2By=700 parts, chosen because of denominators 7 and 10.

Accounting for concentration of milk,
%28%284%2F7%29x%2B%289%2F10%29y%29%2F700=3%2F5
Simplify this rational equation so it is in a neater linear equation format. This and the 700 Sum equation will be your system to solve for x and y.




----------------------------------------------
%284%2F7%29x%2B%289%2F10%29y=%28700%2A3%29%2F5
%284%2F7%29x%2B9%2F10%29y=140%2A3
70%2A%284%2F7%29x%2B70%289%2F10%29y=70%2A140%2A3
40x%2B63y=7%2A14%2A3%2A100
40x%2B63y=29400---------one equation for the system
Try substituting with y=700-x.
40x%2B63%28700-x%29=29400
40x%2B63%2A700-63x=29400
-23x=29400-63%2A700
23x=63%2A700-29400=14700%0D%0A%7B%7B%7B23x=14700
x=14700%2F23=
x=639
I'm getting very close to 639, but may have a mistake somewhere.
y=61, x=639.
Seems very near to choice (b).