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Brad went to a lemonade stand and decided to buy some lemonade. The lemonade stand had two different sizes of cups available. Brad bought a small cup of lemonade, which was 3/8 of the total amount he wanted to buy. He then decided to buy a larger cup of lemonade, which was 0.7 times the amount left after buying the small cup. Finally, Brad realized he still had some money left and decided to buy an additional 12 units of lemonade. Can you determine how much lemonade Brad initially wanted to buy?

 Aug 1, 2023
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1. Brad buys a small glass of lemonade, which is 3/8 of the total amount he wants to buy. Let's say the total amount of lemonade that Brad initially wants to buy is denoted by "x". Based on the information provided, Brad purchases a small 3/8 x cup. Therefore, the amount of lemonade in a small glass can be calculated as (3/8) * x. 

2. Brad then decides to buy a larger glass of lemonade, which is 0.7 times the amount left after buying the smaller glass. 
After buying the small cup, Brad is left with (1 - 3/8) = 5/8 of the amount of lemonade he originally wanted. The large mug he bought was 0.7 times the remaining amount. Therefore, the amount of lemonade in the largest glass can be calculated as (0.7) * (5/8) * x. 3. Finally, Brad decides to buy 12 more units of lemonade. The additional cup bought this time has nothing to do with the previously purchased cup. Therefore, we can add 12 units to the total amount of lemonade he already has. Putting it all together, we can create the equation: 
(3/8) * x + (0.7) * (5/8) * x + 12 = x 

To solve for x, we can simplify and solve the equation: 
(3/8 + (0.7) * (5/8)) * x + 12 = x 
((3 + 0.7*5)/8) * x + 12 = x 
(3 + 3.5)/8 * x + 12 = x 
6.5/8 * x + 12 = x 
6.5x/8 + 12 = x 
6.5x + 96 = 8x 
96 = 8x - 6.5x 
96 = 1.5 times 
x = 96/1.5 
x = 64 

Therefore, Brad initially wants to purchase 64 units of lemonade. 

 Aug 1, 2023

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