Hot Chocolate and Coffee question

Question

Lilya fills a cup with hot chocolate. She drinks 1/2 cup and then pours coffee into the cup until it is full. She stirs the new mixture and drinks 1/2 cup and then fills the cup again with coffee. Lilya continues this pattern until she has consumed 2 full cups. When she next fills the cup with coffee, what percentage of the original hot chocolate remains in her cup?

Answer 1

You start with 1 cup hot chocolate.

After drinking half (total of one half cup) and adding coffee, you multiply 1 cup times 1/2 to give you 1/2 cup

After drinking half of that (total of one cup) and adding coffee, you have 1/2 of the 1/2 cup hot chocolate, so 1/2 x 1/2 cup = 1/4 cup

After drinking half of that (total of one and one half cups) and adding coffee, you have 1/2 of the 1/4 cup hot chocolate, so 1/2 x 1/4 cup = 1/8 cup

After drinking half of that (total of two cups) and adding coffee, you have 1/2 of the 1/8 cup hot chocolate, so 1/2 x 1/8 cup = 1/16 cup or 6.25%

Answer 2

In order for Lilya to drink 2 full cups, you know she would have to drink from her beverage 4 times (4 sets of 1/2 cup).

the first drink leaves her with 50% hot chocolate (H) left in the cup.  the 2nd drink she would consume 1/2 of the 50%/50% mixture so would be left with 25% H (and when she refills 75% C (coffee)). 3rd drink, 1/2 of the 25% would be 12.5% and 4th drink, 1/2 of 12.5% would be 6.25% hot chocolate left.

 

The 100% * 1/2 * 1/2 * 1/2 * 1/2 = 6.25%