SOLUTION: Hello, My name is Traci and I am the mother of 7th grade pre-algebra student. She recently brought home a question and while I am usually able to help her with homework (after I

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Question 814624: Hello,
My name is Traci and I am the mother of 7th grade pre-algebra student. She recently brought home a question and while I am usually able to help her with homework (after I re-learn how to do it myself), I am really stuck with this one. We have tried "acting it out with colored water," ratios, fractions and scouring the internet, but I am still at a loss to wrap my brain around this question so that I may adequately explain it to my daughter and lead her to discovery the solution on her own. Any help will be much appreciated!
Here goes:
I have one large pitcher containing 1 quart of lemonade and a second large pitcher containing 1 quart of iced tea. I pour 1 pint of lemonade into the iced tea pitcher and thoroughly mix it, and then pour 1 pint of the mixture back into the lemonade pitcher.
1. Is there more iced tea in the lemonade or more lemonade in the iced tea? Justify mathematically.
2. If the process is repeated a second time, how many ounces of lemonade will be in the original iced tea pitcher?
3. Is it possible to make both mixtures into 1/2 lemonade and 1/2 iced tea, using the same process repeatedly? Why or why not?
Thanks in advance for any help on this one!

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

know as children we would mix two sodas "back and forth" from one glass to another 

thinking we both ended up with the same taste :) Good luck to You both.

Note:  1Qt = 2Pints

pitcher A - 1 quart of lemonade 

pitcher B - 1 quart of iced tea

pour 1 pint of lemonade into the iced tea pitcher B =  2:1

thoroughly mix it, and put 1 pint back into the lemonade pitcher. 

A = 1ptsL + [  2/3pts IT +1/3ptsL ]  

A =  2:1  and  B = 2:1

1. Is there more iced tea in the lemonade or more lemonade in the iced tea?  same

2. If the process is repeated a second time...

first  B = 4/3pts IT + 2/3 pts L +[2/3ptL + 1/3ptIT} =   5:4

and then 1Pt back..

 A = 2/3ptL + 1/3ptIT + [5/9IT + 4/9 ptL ]

A =   5:4       B =    5:4

 

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