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1. 160 kg of 40% cream to standardize to 32% cream, how much skimmed milk should be added?

Mass Balance Approach

let x = kg skimmilk

y = kg of 32% cream

Mass Balance (mass into the process = mass out of the process) 160 + x = y

Component Balance for Fat (fat into the process = fat out of the process)
.40 (160) = .32 (y) which says 40% of 160 kg comes in and 32% of y goes out
.40 (160) = .32(160+ x) substituting our equation for y
.32x = 64 - 51.2
x = 40 kg skimmilk

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2. How much cream at 35% fat should be added to 500 kg of milk at 4% fat to obtain cream at 10% fat?

Mass balance approach

let x = kg 35% cream

y = kg of 10% cream

Mass Balance x + 500 = y mass in = mass out

Component Balance for Fat
x (.35) + 500 (.04) = y (.10) again, fat in = fat out
x (.35) + 20 = x(.10) + 50
25 x = 30
x = 120 kg of 35% cream

Pearson square approach to above problem
A shortcut for 2-component mass balances
Place desired percentage in the centre of a rectangle
Place percentage composition of two available streams in left corners of rectangle
Cross subtract lower from higher numbers for right corners of triangle (higher number - lower number)
Use right corners as ratios of two streams
Using the above problem:

Component ...................................Mass

35 ................... 6

............10 .........

4 .....................25............................ 500

....................--------..........................-------
........................31

35% cream = 500 x 6 = 120 kg
......................_______
............................25