Mixture replacement math help.

Question

A container contains 64 liters of pure milk. A replacement process takes place three times. A person takes out 16 liters of milk from the container and replaces it with 16 liters of water. Then 16 liters of the mixture is taken out and replaced with 12 liters of wine. Then 8 liters of the mixture is taken out and replaced with 14 liters of water.

A. What is the quantity of milk left after the final replacement?

B. What is the ratio of milk:water:wine in the container after the final replacement?

Answer 1

just track the amount of each

We start with 64 liters of milk.

We remove 16 liters of milk and replace with 16 liters of water, so we have

64 - 16 = 48 liters of milk and 16 liters of water, for 64 liters total

We remove 16 liters of this mixture.

We now have

48 - 16 * 48/64 = 48 - 12 = 36 liters of milk and

16 - 16 * 16/64 = 12 liters of water

12 liters of wine are added, so we have 36 + 12 + 12 liters = 60 liters total

We remove 8 liters, so we have

36 - 8 * 36/60 = 31 1/5 liters of milk

12 - 8 * 12/60 = 10 2/5 liters of water

12 - 8 * 12/60 = 10 2/5 liters of wine

We now add 14 liters of water, so we have

31 1/5 liters of milk

10 2/5 + 14 = 24 2/5 liters of water

10 2/5 liters of wine

a) 31 1/5 liters of milk are left after replacement

milk:water:wine =

31 1/5:24 2/5:10 2/5 =

156/5:122/5:52/5 =

156:122:52 =

78:61:26