Thread: percentages

1. percentages

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 a pint of 2 percent milk. How much of each type of milk should I use ?

2. Hello, lilikoipssn!

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

Let $\displaystyle x$ = amount of 1% milk.
. . It contains: .$\displaystyle \frac{1}{100}x$ pints of fat.
Then $\displaystyle \frac{1}{3} - x$ = amount of 4% milk.
. . It contains: .$\displaystyle \frac{4}{100}\left(\frac{1}{3} - x\right)$ pints of fat.
Hence, the mixture contains a total of: .$\displaystyle {\color{blue}\frac{1}{100}x + \frac{4}{100}\left(\frac{1}{3} - x\right)}$ pints of fat.

But we know that the mixture will be $\displaystyle \frac{1}{3}$ pints which is 2% fat.
. . It contains: .$\displaystyle \frac{2}{100}\left(\frac{1}{3}\right) \;=\;{\color{blue}\frac{2}{300}}$ pints of fat.

We just described the final amount of fat in two ways.

. . There is our equation . . . $\displaystyle \frac{1}{100}x + \frac{4}{100}\left(\frac{1}{3}-x\right) \;=\;\frac{2}{300}$