Question 1117313: Beth has a bottle half filled with water. She drinks two-thirds of the water and gives the remaining water, 240 ml, to Mary. How much water would the bottle contain if it were full?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = amount of water in mL if the bottle were full
x/2 = amount of water if bottle is half filled
Beth has x/2 mL of water and drinks 2/3 of that. So she drinks (2/3)*(x/2) = (2x)/(3*2) = 2x/6 = x/3 mL of water. There is (x/2) - (x/3) = (3x/6) - (2x/6) = x/6 mL left over.
Put another way, we can think of it as Beth drinking 2/3 of the water so there's 1/3 of it left. This means (x/2)*(1/3) = (x*1)/(2*3) = x/6 mL water left
We know that there's 240 mL of water left over, so x/6 = 240 is the equation we need to solve. To solve this, multiply both sides by 6. This is to undo the division.
x/6 = 240
6*x/6 = 6*240
x = 1440
There would be 1440 mL of water if the bottle was completely filled.
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