you make one pitcher of iced tea and one pitcher of lemonade for a party. just before the party starts, you catch a little mischievous child mixing the two beverages. the child says that only one cup of the iced tea was taken and put in the lemonade. then, the child took only one cup of the lemonade-tea mixture that was just created and put it back into the pitcher of iced tea, hoping that no one would notice what had been done. is there now more lemonade in the iced tea or more iced tea in the lemonade? yeah

more lemonade in the iced tea

Step-by-step explanation:

Let's suppose you start with 1L of lemonade and 1L of ice tea in different containers. And also supose that the cup has dimensions for 0.1L.

If you put 0.1 L of the tea and put it in the lemonade, then you have:

0.9 L of tea in container 1, and 1L of lemonade + 0.1L of tea on container 2.

then, the container 2 has 1.1L of a mixture, where 1/1.1 = 0.909, so the solution has a 90.9% of lemonade, and a 9.1% of ice tea.

if the distribution is homogeneous, when the kid the kid takes 0.1L of this mixture, then the 0.1L is: 0.0909L of lemonade, and 0.0091L of ice tea.

this means that in container 1 you will have:

0.9L of tea + 0.00091L of tea + 0.0909L of lemonade

so: 0.90091 L of tea and 0.0909L of lemonade.

In container 2 you will have 1L of lemonade - 0.0909 L of lemonade and +0.1L of tea - 0.0091L of tea

this is:  0.9091L of lemonade, and 0.0909L of tea

So the amount of tea in the lemonade is the same as the amount of lemonade in the tea.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80