Mixing liquids with different sugar concentration

Question

Jim has two, 2 liter, bottles of soda. bottle #1 has 50grams of sugar. Bottle #2 has 0grams of sugar. Jim starts drinking from soda bottle #1 in 10milliliter sips. Every time Jim takes a sip of bottle #1 he refills it with 10milliliters of the soda from bottle #2. When bottle #2 is empty how many grams of sugar will be in the soda in bottle #1?

Answer 1

Hi Chase,

 

Did you need any more clarification on the answer that Mark O. provided?

Thanks,

Anthony

Answer 2

Hi Chase,

 

We need to assume that Jim always allows enough time between sips to allow the soda with the sugar to mix to be homogeneous. He takes 10 mL sips, which is equal to 0.01 Liter. How many 10-mL sips does it take to make 2L? The answer is 2/0.01 = 200 sips.

 

Each time Jim takes a 10-mL sip, he takes 1/200 of the sugar in the solution. He leaves behind 199/200 of the sugar. He does this 200 times. So, after 200 sips, the amount of sugar left in the 2L bottle will be

 

mass_remaining = (50 g sugar)(199/200)²⁰⁰ = (50 g)(0.367) = 18.4 g of sugar