The diary farmer should use 1000 pounds of 85 % protien and 55 % of 200 pounds to make 1200 pounds of a high-grade 80% protein ration
Solution:
Let the amount of 85 % protien supplement be "x"
Then amount of 55 % protien be (1200 - x)
According to given question,
85 % of "x" protien supplement + 55 % of 1200 - x protien used to get 80 % of 1200 pounds
85 % of x + 55 % of (1200 - x) = 80 % of 1200
[tex]\frac{85}{100} \times x + \frac{55}{100} \times (1200 - x) = \frac{80}{100} \times 1200\\\\0.85x + 0.55(1200 - x) = 960\\\\0.85x + 660 - 0.55x = 960\\\\0.3x = 960 - 660\\\\0.3x = 300\\\\x = 1000[/tex]
Pounds of 85 % protien used = 1000 pounds
Then pounds of 55 % protien used = 1200 - 1000 = 200 pounds
Thus he should use 1000 pounds of 85 % protien and 200 pounds of 55 % protien to get 1200 pounds of a high-grade 80% protein ration
