Within the combination of these two pitchers of orange-juice concentrate, finding the proportion of orange juice contained within the final mixture would be calculated by adding up the amount of juice in each then converting the amount into a fraction. This can be done by converting the ⅓ and ⅖ into numbers then adding the numbers and making a fraction with that answer of 1200 then simplifying that to get 11/30.
We first have to find the amount of juice in each pitcher. If we want to find how much ⅓ of a pitcher is we have to divide 600mL by 3, which equals 200mL, the amount of juice in pitcher one. To find the amount of juice in the second pitcher we have to divide 600mL by 5, which equals 120mL, ⅕ of the pitcher. We want to find ⅖ of the pitcher. So we have to multiply 120mL by 2 to get ⅖ of a pitcher because ⅕ is 120mL. 120mL times 2 equals 240mL.
We can easily find the amount of water in both pitchers by subtracting 600mL by either 240mL or 200mL. That would equal pitcher 1 to have 400mL of water and pitcher 2 to have 360mL of water. We know that both full pitchers are being added together in a large pitcher. So 600mL plus 600mL equals 1200mL. We want to find the total amount of orange juice in the large pitcher so we have to add 200mL and 240mL, which equals 440mL. So that amount of orange juice in the large pitcher is 440/1200. We then have to simplify that to 44/120 to 22/60 to 11/30. So 11/30 is the answer.
So we first find the amount of orange juice in each pitcher. Then, we add up the two pitchers to get the larger pitcher. Next, we add the amount of orange juice in each small pitcher to find the amount of juice in the large pitcher. Finally, we simplify to get 11/30. It cannot be any of the other answers because 11/30 cannot simplify any further and all the other fractions are either smaller or larger than this answer. So the answer ends up with 11/30.