if a bottle holding 3 liters of milk contains 3.5% butterfat,How much skimmed milk must be added to dilute the milk to 2% butterfat

amount of skimmed milk added --- x L

.035(3) +0.0x = .02(x+3)
.105 = .02x + .06
.02x = .045
x = 2.25

add 2.25 L

check:
3.5% of 3 L is .105 L of fat
adding 2.25 L of no fat milk gives us
5.25 L containing still only .105 fat
rate of fat = .105/5.25 = .02 as required

Well, let's calculate this using the power of mathematics and a pinch of humor! Since we want to dilute the milk from 3.5% butterfat to 2% butterfat, it means we need to decrease the percentage. Now, since the quantity will remain the same, we know that the butterfat amount needs to decrease.

To solve this, we can set up a proportion. Let's call the unknown quantity of skimmed milk "x". So, we'll have:

3.5 / 100 = 2 / (3 + x)

Now, let's cross-multiply and solve for x:

3.5(3 + x) = 2(100)
10.5 + 3.5x = 200
3.5x = 200 - 10.5
3.5x = 189.5
x = 189.5 / 3.5
x ≈ 54.14

So, you will need approximately 54.14 liters of skimmed milk to dilute the 3 liters of milk to 2% butterfat. But hey, don't worry too much about the decimal points, just grab a big jug and start pouring!

To determine the amount of skimmed milk that needs to be added to the bottle of milk to dilute it to 2% butterfat, we can follow these steps:

Step 1: Calculate the initial amount of butterfat in the bottle of milk.
Initial butterfat = 3 liters × (3.5% / 100) = 0.105 liters

Step 2: Determine the final desired amount of butterfat in the diluted mixture.
Final butterfat = 2% / 100 = 0.02

Step 3: Set up an equation to solve for the amount of skimmed milk needed.
Initial butterfat / Total volume = Final butterfat

Let's assume that "x" represents the amount of skimmed milk to be added.

0.105 liters / (3 liters + x) = 0.02

Step 4: Solve the equation for "x".
0.105 = 0.02 × (3 liters + x)
0.105 = 0.06 + 0.02x
0.02x = 0.105 - 0.06
0.02x = 0.045
x = 0.045 / 0.02
x ≈ 2.25 liters

Therefore, you would need to add approximately 2.25 liters of skimmed milk to dilute the milk to 2% butterfat.

To solve this problem, we first need to understand the butterfat content in the original 3 liters of milk and the desired butterfat content of the diluted mixture. Let's break it down step by step:

Step 1: Calculate the amount of butterfat in the original milk.
The original milk contains 3 liters with a butterfat content of 3.5%. To find the amount of butterfat, we can multiply the volume of milk (in liters) by the percentage of butterfat in decimal form:

Butterfat in original milk = 3 liters × 3.5% = 0.035 liters

Step 2: Determine the desired amount of butterfat in the diluted mixture.
The goal is to dilute the milk to a 2% butterfat content. We need to find out how much butterfat should be in the final mixture after adding skimmed milk.

Desired butterfat in the final mixture = 3 liters × 2% = 0.06 liters

Step 3: Calculate the amount of skimmed milk required to achieve the desired butterfat content.
Now, we need to calculate how much skimmed milk should be added to achieve the desired butterfat content in the final mixture. This can be done by subtracting the amount of butterfat in the original milk from the desired amount of butterfat in the final mixture:

Amount of skimmed milk to be added = Desired butterfat - Butterfat in original milk
= 0.06 liters - 0.035 liters
= 0.025 liters

Therefore, you would need to add 0.025 liters (or 25 milliliters) of skimmed milk to dilute the 3 liters of milk to a 2% butterfat content.