SOLUTION: A chef needs to mix a 45% fat content cheese with a 20% fat content cheese to obtain 30 grams of a cheese mixture that is 30% fat. How many grams of each kind of cheese must be use

Question 10413: A chef needs to mix a 45% fat content cheese with a 20% fat content cheese to obtain 30 grams of a cheese mixture that is 30% fat. How many grams of each kind of cheese must be used?
Answer by calbreez(9) (Show Source): You can put this solution on YOUR website!
Let the amounts of the 2 cheeses be x and y grams
0.45x+0.2y = 0.3*30 (1) and x + y = 30 (2)
Simplifying (1):
0.45x + 0.2y = 9
45x + 20y = 900
9x + 4y = 180 (3)
Multiply (2) by 4:
4x + 4y = 120 (4)
Subtract (4) from (3):
5x = 60
x = 12
Substitute x = 12 into (2):
12 + y = 30
y = 18
Therefore the chef needs 12 g of 45% fat content cheese and 18 g of 20% fat content cheese.

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