How many ounces of a 22% alcohol solution must be mixed with 23 ounces of a 5% solution to produce a 10% alcohol solution? Round to the nearest tenth of an ounce. Can somebody explain how to do this problem?

- anonymous

- katieb

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- amistre64

i can do it; but splaining it might be a challenge :)

- amistre64

a + 23 = total amount of liquid
a(.22) +23(.05) = (a+23)(.10)
.22a + 1.15 = .10a + 2.3
.12a = 2.30 - 1.15 = 1.15
a = 1.15/.12 = 115/12 = 9.5833....

- anonymous

trying it...

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## More answers

- anonymous

That got the right answer...and your equation does make sense to me...I got the stuff on the left side of the equal sign right, but had messed up on the right side of the equal sign. I had .10x on the right side. Can you explain why this was wrong, and I needed your a+23 times .1Ox? :P

- anonymous

times just .10, that is

- amistre64

a+23 is the total amont of the , im assuming liguid, that the system holds.
so (total amount) * (.10) gives us the volume of solution and % content

- anonymous

Ah. I guess I just had the % content on the right side, and did not have the amount times .1 to give me the volume...

- amistre64

the amount of 23 was stated inte problem

- anonymous

I know....I hope I can remember your equations for these type of problems, for my math test tomorrow. :)

- amistre64

the are all of a basic form:
amount(%) of one item + amount(%) of another item = total amount(%) of ending item

- anonymous

I'm copying this now and saving it...:)

- amistre64

if amount is money, we get interest

- amistre64

20(.05) + 30(.10) = 50(x)

- anonymous

I'm actually good at simple interest problems...:)

- amistre64

then consider these simple interests problems :)

- amistre64

$a(.22) + $23(.05) = $(a+23)(.10)

- anonymous

Uh...the problem of relating simple interest to mixture problems for me...is that I actually have a little diagram circle that I write and label to help me with simple interest problems...your above sentence is kinda confusing...without a story problem to go with it, that is...

- amistre64

story problem then:
if $23 is invested at 5%, how much money needs to be invested at 22% to get as much interest at a single account at 10%

- anonymous

That makes your equation make more sense to me..:)

- anonymous

But now the a+23 does not seem like it would equal a 'single account'...

- anonymous

maybe I'm thinking too hard...

- anonymous

:P

- anonymous

I guess I'm stuck on, just doing the .1 times something, would equal a 'single account' or the 'final solution'...

- anonymous

that tends to be my train of thought right now, for some reason..

- anonymous

Bu t thanks anyway. :)

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