I need help with a math problem/medical calculation

I am hoping someone will help me understand this math problem.

How much 50% dextrose must be added to 1L lactated Ringer solution to make a solution that contains 5% dextrose?

c1v1 = c2v2 (concentration 1 x volume 1 = concentration 2 x volume 2)

So..

50x = 5(1000 + x)

solve for x

I am told that x = 110ml. I cannot figure out how to reach that answer with that equation. I want to know the steps taken to reach that answer. The x on both sides is throwing me off for some reason.

x = 1000/9 = 111.111

Round down

a reply to: paperdoll

50x = 5(1000 + x)
50x = 5000 + 5x
45x = 5000
x = 5000/45
x = 111.1111111 (repeating)

rounded down is 110.

EDIT:

Here's the explanation:

1. expand the right side: 50x = 5000 + 5x
2. now subtract 5x from both sides (and now you have x on just the left side): 45x = 5000
3. divide both sides by 45 to leave x by its lonesome on the left: x = 5000/45
4. simply the fraction by dividing the numerator (the top) by the denominator (the bottom): x = 111.1111...
5. Round down the result to the nearest 10 ml.

^^^^^^^^^^^^^^^

What they said 😜

Thanks!

Or just mix it up the same and take out 10% total volume

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