# five vessels have equal capacities. Each vessel contains some milk. the ratio of the quantities of milk in these vesseles is 3:4:5:6:7 . the total quantity of milk is 60% of the combined capacity of the vessels. How many vessels contain at least 50% milk?

How to frame an eequation to solve

## 3+4+5+6+7 = 25

So, the milk in the vessels is
3x,4x,5x,6x,7x

If the capacity of each is z, then

25x = 0.6*5z = 3z
x = 0.12z

So, in terms of a full vessel, the amounts of milk in each of the vessels is

.36, .48, .60, .72, .84

Looks like 3 of them are over 50% full.

## To solve the problem, we can set up the equation as follows:

Let x be the capacity of each vessel.

Since the ratio of the quantities of milk in the vessels is 3:4:5:6:7, we can express the quantities of milk in the vessels as:

Milk in the first vessel = (3/18) * x
Milk in the second vessel = (4/18) * x
Milk in the third vessel = (5/18) * x
Milk in the fourth vessel = (6/18) * x
Milk in the fifth vessel = (7/18) * x

According to the problem, the total quantity of milk is 60% of the combined capacity of the vessels, which means:

(3/18) * x + (4/18) * x + (5/18) * x + (6/18) * x + (7/18) * x = (60/100) * (5 * x)

Now, we can simplify and solve for x:

(60/ 100) * 5 * x = (3/18) * x + (4/18) * x + (5/18) * x + (6/18) * x + (7/18) * x

(3/10) * 5 * x = (6/18) * x + (8/18) * x + (10/18) * x + (12/18) * x + (14/18) * x

(3/10) * 5 * x = (50/18) * x

Cross-multiplying:

(3/10) * 5 * x * 18 = 50 * x

15 * x * 18 = 50 * x

Now, we can solve for x:

270 * x = 50 * x

Dividing both sides by x:

270 = 50

Therefore, there is no valid solution to this problem.

## To solve this problem, we can follow these steps:

1. Let's assume the capacity of each vessel is represented by 'x' units.
2. The ratio of milk quantities in the vessels is given as 3:4:5:6:7.
3. So, the quantities of milk in the vessels can be calculated as:
- Vessel 1: (3/18)x
- Vessel 2: (4/18)x
- Vessel 3: (5/18)x
- Vessel 4: (6/18)x
- Vessel 5: (7/18)x
Note: The denominators (18x) represent the sum of the ratios (3+4+5+6+7).
4. The total quantity of milk is given as 60% of the combined capacity of the vessels. So, we can set up the equation:
(3/18)x + (4/18)x + (5/18)x + (6/18)x + (7/18)x = 0.60 * (5x)
Simplifying the equation:
(25/18)x = 0.60 * (5x)
5. By simplifying further, we find:
(25/18)x = 0.30x
6. To solve for 'x', we can cross-multiply and solve as follows:
25x = 0.30 * 18x
25x = 5.40x
Subtracting 5.40x from both sides:
25x - 5.40x = 0
19.60x = 0
7. Solving for 'x':
x = 0
Since the capacity of the vessel cannot be zero, this means there is an error in the problem statement or calculations. Please double-check the given information for accuracy.

Once the error is corrected and the value of 'x' is obtained, we can determine the number of vessels that contain at least 50% milk by comparing their quantities of milk with half of the capacity.

## Oh, I love a good milk mystery! Let's solve this riddle with some humor, shall we?

First, let's assume the capacity of each vessel is C. So their capacities are C, C, C, C, and C respectively.

Now, the ratio of milk quantities in the vessels is 3:4:5:6:7. We can express this as:

3C : 4C : 5C : 6C : 7C

According to the question, the total quantity of milk is 60% of the combined capacity of the vessels. So, let's calculate that:

Total Quantity of Milk = 60% of (5C + 6C + 7C + 4C + 3C)
= 0.6 * (25C)
= 15C

Now, we know that the Total Quantity of Milk is equal to 15C. We also know that the combined capacity of the vessels is 5C + 6C + 7C + 4C + 3C = 25C.

But the question asks how many vessels contain at least 50% milk. Hmm, let's put on our thinking caps and figure this out.

If a vessel contains at least 50% milk, that means the quantity of milk in that vessel is greater than or equal to 0.5 * C (50% of its capacity).

So, we need to find out how many vessels have a milk quantity greater than or equal to 0.5 * C.

Let's see, the ratio of milk quantities is 3:4:5:6:7. We find out which ratios are greater than or equal to 0.5:

3/1 >= 0.5 (Yes!)
4/1 >= 0.5 (Yes!)
5/1 >= 0.5 (Yes!)
6/1 >= 0.5 (Yes!)
7/1 >= 0.5 (Yes!)

Aha! All the ratios are greater than or equal to 0.5. That means all the vessels contain at least 50% milk.

So, the number of vessels that contain at least 50% milk is 5.

I hope my milk calculations made you smile!