Problem Solving

kaudes11114 wrote:According to the directions given on the frozen orange juice concentrate can, 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

How's this: To make orange juice, we combine 1 part concentrate with 3 parts water. Our goal is to create 200 6-ounce servings of orange juice. How many 12 ounce cans of concentrate are required to achieve this goal?


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 [spoiler]x=25[/spoiler]
So, the answer is A

Cheers,
Brent

A "6-ounce serving" denotes a certain volume of a serving. This is analogous to a 185-ml serving.
We want 200 of those servings.
In other words, we want 200 glasses of orange juice, where each glass contains 6 ounces (185 ml) of orange juice.

Cheers,
Brent