# Pre-Calc mixture problem: transferring liquids from one cup back to the other

#### beegillman76

##### New member
I have a mixture problem that involves transferring liquids from one cup back to the other, Coke and Sprite. Basically both start off pure at 355 ml in each glass. The first step in the problem asks you to take 5ml of liquid from the sprite glass and put it into the coke glass. It asks for a percentage of coke in the coke glass. If my math is correct 360x=355 and x =.9861 or 98.61%.
The second part asks you to take 5ml of the diluted coke and add it to the sprite glass to find the percentage of coke in the sprite glass.

I can't seem to get this into problem form.... I understand that I am starting with 350 ml of a 100% soln. of sprite and adding in 5ml of coke that is 98.61% coke (4.93ml of 5), but i can't seem to make it into a formula.

#### Otis

##### Senior Member
I have a mixture problem that involves transferring liquids from one cup back to the other, Coke and Sprite.

Basically both start off pure at 355 ml in each glass. The first step in the problem asks you to take 5ml of liquid from the sprite glass and put it into the coke glass. It asks for a percentage of coke in the coke glass. If my math is correct 360x=355 and x =.9861 or 98.61%.

The second part asks you to take 5ml of the diluted coke and add it to the sprite glass to find the percentage of coke in the sprite glass.

I can't seem to get this into problem form.... I understand that I am starting with 350 ml of a 100% soln. of sprite and adding in 5ml of coke that is 98.61% coke (4.93ml of 5), but i can't seem to make it into a formula.
Your first calculation is correct. 355 ml of pure Coke mixed with 5 ml of Sprite yields 360 ml of a solution containing 98.61% Coke.

You then correctly calculated that the percentage of Coke in 5 ml of the mixture is 4.98 ml.

So, when you add the 5 ml of mixture into the remaining volume of pure Sprite, what is the resulting volume? How much Coke went into that mixture? (You've already calculated this.)

Use these two values to determine the percent in the same way that you used 360 (whole) and 355 (part) to determine 98.61%

Hope this helps, but if you're still stuck, please show what you tried. #### beegillman76

##### New member
So... Would I set the 355 equal to 4.93 because that's the concentration of the 5 ml that I'm adding back?
355x=4.93

#### Otis

##### Senior Member
Would I set the 355*x equal to 4.93 ... ?

355x=4.93
Yes.

Your equation says that x% of 355 is 4.93. Solve for x.