math

A and B farm A produces milk with 3 ½ percent fat and farm B produces milk with 4 ¾ percent fat.
(a) Determine
(i) The total mass fat in 50 kg milk from farm A and 30 kg of milk from farm B
(ii) The percentage of fat in a mixture of 50 kg of milk from A and 30 kg of milk from B
(b) Determine the range of values of mass of milk from farm B that must in a 50 kg mixture so that the mixture may have at least 4 percent fat.

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1. (i) 50(0.035) + 30(0.0475) = 3.175
(ii) 3.175/(50+30) = 0.03968 = 3.97%

.035x + .0475(50-x) >= 0.04*50
x <= 30

That is, with 30kg from A and 20kg from B, the result is exactly 4% fat

Since A's content is less than 4%, using any more of A will reduce the result below the desired 4% mix. Having less than 30kg from A will mean more than 20kg from B, raising the fat content above 4%.

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