I want to dilute 500ml of 35% cream into 10% by adding 1% milk. How much milk must I add?

Answer 1

I'm assuming the percentages are the percentage of milk-fat.

You've got 500 × 35% = 175 mL of milk-fat right now.

You're adding x × 1% = 0.01x mL of milk-fat when you add x mL of 1% milk.

The resulting mixture will be (x + 500) mL, of which 10% will be milk-fat: (x + 500) × 10%.

500(.35) + x(.01) = (x + 500)(.10)

175 + .01x = .1x + 50

125 = .09x

1388.89 mL of 1% milk

Answer 2

The amount of fat in 500 ml of 35% cream = .35*500;

If we add an amount V of 1% milk, we increase the amount of fat in the mixture by .01*V, so the new total fat amount will be .35*500 + .01*V. The new total volume will be 500 + V, so the final concentration is

(.35*500 + .01*V)/(500 + V)

and this must equal .10, then the equation to solve is

(.35*500 + .01*V)/(500 + V) = .1

(.35*500 + .01*V) = .1*(500 + V)

175 + .01*V = 50 + .1*V

.09V = 125

V = 1388.9 ml

Answer 3

You need to figure out what to equate. Try equating the fat content before and after mixing (because it won't change). Setting the amount of 1% milk to x, you would get

0.35(500) + 0.01x = 0.1(x + 500)

Solve that for x.