Xperiamammonidn
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A processing plant is producing 100 kg of minced meat, which must contain 15% of fat. If this is to be made up from boneless cow beef with 23% of fat and from boneless bull beef with 5% of fat, how much of each beef are required to mix?​

Sagot :

Talingtingklaineleyidn

Let the proportions be A of cow beef to B of bull beef. Then by a mass balance on the fat,

Mass in Mass out

A x 0.23 + B x 0.05 = (A + B) x 0.15.

that is A(0.23 - 0.15) = B(0.15 -0.05).

A(0.08) = B(0.10).

A/ B = 10/8

or A/(A + B) = 10/18 = 5/9.

100 kg of product will have 55.6 kg of cow beef to 44.4 kg of bull beef.

If the weights of the constituents are A and B and proportions of fat are a, b, blended to give C of composition c:

then for fat Aa + Bb = Cc

and overall A + B = C

of which A and B are unknown, and say we require these to make up 100 kg of C then

A + B = 100

or B = 100 - A

and substituting into the first equation

  • Aa + (100 - A)b = 100c
  • or A(a - b) = 100(c - b)
  • or A = 100 (c-b)/ (a-b)

and taking the numbers from the example

the example are in the picture

View image Talingtingklaineley
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