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mixtures

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mixtures

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please solve
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According to the directions on a can of orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of the concentrate are required to prepare 200 6 ounce servings of orange juice.
A. 25
B. 34
C. 50
D. 67
E. 100
The ratio of concentrate to water in the juice mixture = 1:3.
Thus, concentrate = 1/4 of the total amount of juice.
Since 200 6-ounce servings are to be prepared, the total amount of juice to be prepared = 200*6 = 1200 ounces.
Since concentrate constitutes 1/4 of the total, the amount of concentrate needed = 1/4 * 1200 = 300 ounces.
Since each can = 12 ounces, the number of cans needed = 300/12 = 25.

The correct answer is A.

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According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce can of the concentrate are required to prepare 200 6-ounces serving of orange juice?
a)25
b)34
c)50
d)67
e)100
This can be solved using equivalent ratios.
The first part tells that, for every 1 can of concentrate, we can make 4 cans of juice.
Let's be even more generic, for 1 volume of concentrate, we can make 4 volumes of juice.

Okay, now notice that we have a problem with the volume mismatch in the question. It involves 12-ounce cans of concentrate and 6-ounce servings.
So, let's reword the question. Instead of making 200 6-ounce servings of juice, let's make 100 12-ounce servings of juice. We're still making the same amount of juice.

We're now asking, "How many 12-ounce cans of the concentrate are required to prepare 100 12-ounce serving of orange juice?

We'll solve this question using equivalent ratios.

(volume of concentrate)/(volume of juice): 1/4 = x/100

Solve for x to get x=25
So, the answer is A

Cheers,
Brent

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Hi Apoorva@5,

This question comes down to how you choose to organize your work and do the math. The individual "steps" involved aren't that tough, but you really have to stay organized to work through this question efficiently.

To start, we're given a "recipe" for making orange juice: 1 can of concentrate + 3 cans of water = 4 CANS of juice

Next, we're told that each "can" = 12 ounces. Combined with the prior info (above)....

1 can of concentrate + 3 cans of water = 4 cans of juice = 48 OUNCES of juice

We're told to make 200 6-ounce servings of juice, which is 200(6) = 1,200 ounces of juice. The question asks how many cans of CONCENTRATE are needed to get us 1,200 ounces (according to the recipe).

Since 1 can of concentrate --> 48 ounces of juice, we can do division to figure out the number of cans needed:

1200/48 = 25 cans of concentrate

Final Answer: A

As I mentioned earlier, there are a number of different ways to "do the math" on this question (and you can even TEST THE ANSWERS), so I'm sure that there will be other approaches mentioned by other posters.

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Rich

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Apoorva@5 wrote:
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce can of the concentrate are required to prepare 200 6-ounces serving of orange juice?
a)25
b)34
c)50
d)67
e)100
Try to bring everything in one unit of measurement.
4 cans of orange juice = 1 can of concentrate + 3 cans of water.
Hence 1 can of juice contains 1 part concentrate and 3 parts water.

Required: How many 12 ounce cans of the concentrate are required to prepare 200 6 ounce servings of orange juice?

We would calculate everything in the form of 12 ounce cans.
200 6 ounce juice = 100 12 ounce juice.

For 100 12 ounce juice, 23 need (1/4)*100 cans of concentrate and (3/4)*100 cans of water. Each measuring 12 ounce

Hence 12 ounce cans of concentrate needed = (1/4)*100 = 25 cans

Correct Option: A

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Concentrate / Total = 1 / (1 + 3) = 1/4 of the total

We've got 200 * 6 = 1200 ounces.

(1/4) of that is concentrate, so we've got (1/4) * 1200, or 300 ounces of concentrate. At 12 ounces per can, that gives us 300 / 12 => 25 cans.

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