Question

4 liters of 2% milk contains 8% cholesterol. A container of skim milk contains 2% cholesterol. How many liters of skim milk need to be added to the 4 liters of 2% milk to create a mixture with 4% cholesterol?

Answer 1

To solve this problem, we can use the following equation:

4+x4×8+x×2​=4

This equation represents the ratio of the total cholesterol to the total volume of the mixture. The numerator is the sum of the cholesterol from the 2% milk and the skim milk, and the denominator is the sum of the volumes of the 2% milk and the skim milk. The equation is equal to 4 because we want the mixture to have 4% cholesterol.

To find x, we can simplify and solve for x:

4+x32+2x​=4

32+2x=16+4x

16=2x

x=8

Therefore, we need to add 8 liters of skim milk to the 4 liters of 2% milk to create a mixture with 4% cholesterol.

Answer 2

To solve this problem, we can set up an equation based on the amount of cholesterol in the mixture.

Let's assume that x liters of skim milk need to be added to the 4 liters of 2% milk.

The amount of cholesterol in the 4 liters of 2% milk is 8% of 4 liters, which can be calculated as (8/100) * 4 = 0.32 liters of cholesterol.

The amount of cholesterol in the x liters of skim milk is 2% of x liters, which can be calculated as (2/100) * x = 0.02x liters of cholesterol.

The total amount of cholesterol in the mixture is the sum of the cholesterol in the 2% milk and the skim milk, which should be equal to 4% of the total volume of the mixture. So, we have:

0.32 + 0.02x = (4/100) * (4 + x)

Simplifying the equation:

0.32 + 0.02x = 0.04(4 + x)

0.32 + 0.02x = 0.16 + 0.04x

0.02x - 0.04x = 0.16 - 0.32

-0.02x = -0.16

Dividing both sides by -0.02:

x = (-0.16) / (-0.02)

x = 8

Therefore, 8 liters of skim milk need to be added to the 4 liters of 2% milk to create a mixture with 4% cholesterol.