Joan poured 7/8 liter of water into a bottle. it filled 5/6 of the bottle. how many liters of water will completely fill the bottle? choices: a. 35/48. b. 1 1/38. c. 1 1/20. d. 1 13/35

Let's set up some equations.

We know that 7/8 of a liter fills up our bottle 5/6 of the way. Thus 7/8=5/6 * b.

Now, let's divide both sides by 5/6 to get b = 21/20. However, none of the answer choices provided are correct. Let's look at each one to determine why it's not correct.

A. This answer is false because 35/48 < 7/8. If 7/8 of a liter doesn't completely fill up the bottle, there is no way that a value less than 7/8 can fill up the bottle - it's impossible.

B. Same case as answer A, but 11/38 instead of 35/48.

C. Same case as answer A, but 11/20 instead of 35/48.

D. This answer however is more than 35/48, so is it correct? No. 113/35 is just over 3. Since 7/8 of a liter almost fills the bottle but does not quite completely fill it, there is no way that adding 2 more liters can fill up the bottle just the tiny 1/6 of the way. That is disproportional and is thus wrong.