According to the directions on a can of frozen organge juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 once cans of concentrate are required to prepare 200 6 ounce servings of orange juice?

a 25
b 34
c 50
d 67
e 100

Answer a 25

Please solve step by step. Thanks.

first, recognize that you want to make a proportion involving 2 quantities: (a) amount of concentrate and (b) amount of JUICE, NOT water.
to take care of (b), note that 1 can of concentrate is used to make 1 + 3 = 4 cans of juice (assuming that the volumes are additive, a necessary assumption here). therefore, the ratio of concentrate to juice is 1:4.

you want to make 200 x 6 = 1200 ounces of orange juice.

set up a proportion:
(ounces of concentrate) / 1200 = 1 / 4

solve:
300 ounces of concentrate

each can of concentrate contains 12 ounces, so 300/12 = 25 cans.

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BACKUP METHOD
you could also solve this problem backwards: try plugging in the answer choices. if you try choice (c), you'll find that the answer is too big, so you can then eliminate choices (c), (d), and (e). at that point, just try one of the two remaining choices. if it works, it's the correct choice; if it doesn't, then the other choice is the correct choice.
or, if you have good number sense, you'll notice that (c) makes exactly twice the required amount of juice. therefore, the correct answer must be (a), which is half of (c).