 # I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how muc

Mathematics

## Question

I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how much of each type of milk should i use ?

• ### 1. User Answers MsEHolt

You should use 2/9 of a pint of the 1% milk and 1/9 of a pint of the 4% milk.

Let x be the amount of 1% milk used.  1% = 1/100 = 0.01; this gives us 0.01x to represent this.

We know that we will use the 4% milk to make up the rest of the 1/3 pint; this gives us 0.04(1/3-x).

Together, they will make 1/3 pint of 2% milk, or 0.02(1/3)

This gives us the equation
0.01x+0.04(1/3-x) = 0.02(1/3)

Multiplying, we have
0.01x+0.04/3-0.04x = 0.02/3

We can multiply everything by 3 to eliminate the fractions:
0.01x*3 + 0.04 - 0.04x*3 = 0.02
0.03x + 0.04 - 0.12x = 0.02

Combining like terms, we have
-0.09x + 0.04 = 0.02

Subtract 0.04 from both sides:
-0.09x + 0.04 - 0.04 = 0.02 - 0.04
-0.09x = -0.02

Divide both sides by -0.09:
-0.09x/-0.09 = -0.02/-0.09

This gives us x = 2/9, so we will use 2/9 of a pint of the 1% milk.

1/3 - 2/9 = 3/9 - 2/9 = 1/9; we will use 1/9 of a pint of the 4% milk.
• ### 2. User Answers oeerivona

The double lathe milk with 2 percent fat concentration, is made by

considering the concentration and amount of each constituent.

The amount of each type of milk to be used in the $$\dfrac{1}{3}$$ pint of double lathe

are;

• $$\dfrac{2}{9}$$ pint of the 1 percent fat milk and  $$\dfrac{1}{9}$$ pint of the 4 percent fat milk.

Reasons:

Let x represent the amount of the milk that contains 1 percent fat in the

volume of the 2 percent fat milk.

Therefore, we have;

The amount of the 4 percent fat milk to be used = $$\dfrac{1}{3} - x$$

$$Amount \ of \ fat = \dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{2}{100} \times \dfrac{1}{3} = \dfrac{2}{300}$$

$$\dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{4 - 9 \cdot x}{300} = \dfrac{2}{300}$$

Therefore;

4 - 9·x = 2

4 - 2 = 9·x

$$x = \dfrac{2}{9}$$

The amount of the 1 percent fat milk to be used for the double lathe, x = $$\dfrac{2}{9}$$

of a pint.

The amount of the 4 percent fat milk to be used for the double lathe = $$\dfrac{1}{3} - x$$

Therefore;

The mount of the 4 percent fat milk = $$\dfrac{1}{3} - \dfrac{2}{9} =\dfrac{1}{9}$$

The amount of the 4 percent fat milk to be used for the double lathe = $$\dfrac{1}{9}$$

pint.