A wine maker has two vats of wine, one with 5% alcohol content and the other with a 20% alcohol content. He wishes to blend them to produce 1L of wine with a 14% alcohol content. How many milliliters of each are required? Show how to use a system of equations to solve this problem.

Question

anonymous · Answer

hmmm what if instead of trying so hard to get 14 he and a friend sit there and test it until theyre content with the alcohol level. (sorry i just needed one point to be in 50 i know this doesnt help.)

anonymous · Answer

wow thanks

mertsj · Answer

Let x = amount of 5% wine to use.
Let y = amount of 20% wine to use
x+y=1
.05x+.20y=.14(1)

anonymous · Answer

then just solve for x and y?

mertsj · Answer

Yes

anonymous · Answer

since I am looking for milliliters though would I change the one to 1000?

mertsj · Answer

It would probably be easiest to multiply the second equation by 100 to get:
5x+20y=14
Then multiply the first equation by -5 and add the two together.

mertsj · Answer

You could change to ml at the end.

anonymous · Answer

ok

anonymous · Answer

so I have the systems x+y=1 and 5x+20y=14
and now I solve for y??

mertsj · Answer

Yes.  Those are the two equations in your system. Solve for both x and y because the problem asks how many mL of each.

anonymous · Answer

ok so I get 4x-19y=13 to start?

mertsj · Answer

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