Orange Juice

Fractal 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 cans of the concentrate are required to prepare 200 6-ounce serving of orange juice?

a) 25
b) 34
c) 50
d) 67
e) 100

Here's one approach:

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 can 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

Fractal 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 cans of the concentrate are required to prepare 200 6-ounce serving of orange juice?

a) 25
b) 34
c) 50
d) 67
e) 100

Could anybody explain me how to solve this exercise? thx

We are given that in order to make orange juice, 1 can of concentrate is used and 3 cans of water. Thus, we can set up the following ratio:
Concentrate: water = x : 3x

We need to determine how many cans of concentrate are needed to prepare 200 6-ounce servings of orange juice, or 200 x 6 = 1,200 ounces.

We can create the following equation to determine the number of ounces of concentrate needed:

x + 3x = 1,200

4x = 1,200

x = 300 ounces

Since there are 12 ounces per can, 300/12 = 25 cans are needed to make 1,200 ounces of orange juice.

Answer: A