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The number of cartons of juices to the number of cartons of milk to the number of cartons of soft drinks is in the ratio of 12 : 5 : 1. There are 66 more cartons of juices than soft drinks. How many cartons of milk are there?

To find the number of cartons of milk, we first need to determine the total number of cartons.

Let's assume the ratio of cartons of juices, milk, and soft drinks is 12x:5x:1x, where x is a common multiplier.

Given that there are 66 more cartons of juices than soft drinks, we have:

12x - 1x = 66

Simplifying this equation, we get:

11x = 66

Dividing both sides by 11, we find:

x = 6

Now, we can substitute the value of x into the ratio to find the number of cartons of each beverage:

Cartons of juices = 12x = 12 * 6 = 72
Cartons of milk = 5x = 5 * 6 = 30
Cartons of soft drinks = 1x = 1 * 6 = 6

Therefore, there are 30 cartons of milk.

To solve this problem, we can start by assigning variables to the number of cartons of juices, milk, and soft drinks. Let's say the number of cartons of juices is 12x, the number of cartons of milk is 5x, and the number of cartons of soft drinks is x.

According to the problem, there are 66 more cartons of juices than soft drinks. This can be expressed as:

12x = x + 66

To solve this equation, we need to isolate x. We can do this by subtracting x from both sides:

12x - x = x - x + 66
11x = 66

Next, we can solve for x by dividing both sides by 11:

11x/11 = 66/11
x = 6

Now that we know the value of x, we can find the number of cartons of milk. Since the number of cartons of milk is 5x, we can substitute x = 6 into this equation:

5x = 5 * 6 = 30

Therefore, there are 30 cartons of milk.