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September 17th, 2018, 11:27 PM  #1 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  Amount of water
Larry used 5/12 of the amount of water in a container to make 30 cups of fruit punch. He then made some cups of tea using the rest of the water left in the container. The amount of water he used for each cup of tea is twice the amount used for each cup of fruit punch. How many cups of tea did he make? I'm not sure how to create an algebraic equation to solve this one. All I know is he has 7/12 water left to make tea, and he is using twice the water. Last edited by skipjack; September 18th, 2018 at 05:19 PM. 
September 18th, 2018, 12:26 AM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
The simplest way to achieve the answer is to work out how many cups of fruit punch he could make with the remaining water, then halve it to obtain the number of cups of tea he could make. My brain spat this out: (7/5)*30/2 = 21 cups of tea 
September 18th, 2018, 04:41 PM  #3 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  
September 18th, 2018, 05:43 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
The quotient of the amounts of water available, namely (7/12)/(5/12) was used, not their product. Water per cup of fruit punch is (5/12)/30 and so water per cup of tea is 2(5/12)/30. Hence the number of cups of tea is given by (7/12)/(2(5/12)/30) = 21. 
September 18th, 2018, 11:40 PM  #5 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
I admit, I took a shortcut, I ignored the denominators completely as I know they cancel out with this specific type of problem.


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