When salted butter is made, salt is added to the butter in a slurry containing water and salt crystals. The slurry contains 50 (m/m)% salt and 50(m/m)% water. The salted butter contains 15 (m/m) % water, 1.5 (m/m) salt and 83.5 (m/m) % solids. Determine:
(a) the amount of salt added per 100 kg salted butter
(b) the amount of the unsalted butter.
(a) To find the amount of salt added per 100 kg of salted butter, we can use the given percentages of salt in the salted butter.
The salt content in the 100 kg salted butter is 1.5% (m/m), which means that in 100 kg salted butter, there is 1.5 kg salt.
So, the amount of salt added per 100 kg salted butter is 1.5 kg.
(b) We are given the percentages of water and solids in the salted butter. To find the amount of unsalted butter, we need to determine the amount of solids that came from the unsalted butter.
In the 100 kg salted butter, the water content is 15% (m/m) and the solids content is 83.5% (m/m). The total mass of unsalted butter can be found by subtracting the mass of salt and water from 100 kg.
Let x be the amount of unsalted butter.
The mass of solids in the unsalted butter will be x - 1.5 (since we have already accounted for the 1.5 kg of salt).
The mass of water in the unsalted butter is 15 - 0.5x (since the slurry contains 50% water).
Now we can set up an equation using the percentages of solids and water:
Mass of solids in unsalted butter / Mass of unsalted butter = Percentage of solids in salted butter
(x - 1.5) / x = 83.5 / (100 - 1.5)
(x - 1.5) / x = 83.5 / 98.5
x - 1.5 = 83.5x / 98.5
98.5x - 148.25 = 83.5x
15x = 148.25
x = 9.88 kg
So, the amount of unsalted butter is 9.88 kg.