Question

A processing plant is producing minced meat, which must contain 15% of fat. If this is to be made up from boneless cow beef trimmings with 25% of fat, 10% protein, 64% water, 1% minerals and from boneless bull beef with 5% of fat, 20% protein, 72% water, 1% mineral. What are the proportions for these to be mixed? Report the ratio of boneless cow beef trimmings to boneless bull beef (e.g., 2:1) Assume the minced meat with 15% fat is to be smoked and then dried to produce beef jerky. Beef jerky requires a water to protein ratio of 1:1. How much jerky will be produced if one starts with 2,000 lbs of 15% fat minced meat?

Answer 1

Given,

Fat content of Boneless cow beef = 25%

Fat content of Boneless bull beef = 5%

Fat content of the mix (minced meat)= 15%

Let mix contains "X" part of cow beef and "Y" part of bull beef.

Mix ratio (X/Y) = ?

We can write,

25 * X + 5 * Y = 15 * (X + Y)

25 * X + 5 * Y = 15 * X + 15 * Y

25 * X - 15 * X = 15 * Y - 5 * Y

10 * X = 10 * Y

X/Y = 1/1 = 1:1

Ratio of cow beef to bull beef required is 1:1

Determination of beef jerky produced:

Weight of minced meat to be used = 2000 lb.

Water to protein ratio in minced meat required to make beef jerky = 1:1

Let us first find water and protein initially present in minced meat,

Water present initially in minced meet = (X * 64 + Y * 72) / (X + Y)

= (1 * 64 + 1 * 72) / (1 + 1)

= 68%

Similarly,

Protein present initially in minced meet = (X * 10 + Y * 20) / (X + Y)

= (1 * 10 + 1 * 20) / (1 + 1)

= 15%

Now in order to have the final water to protein ratio of 1:1 in the beef jerky, water content of the minced meat should be reduced to 15%.

Hence reduction in water = (68-15)% = 53 % = 0.53 * 2000 = 1060 lb

Dry weight of minced meat after reduction in water content = (2000 - 1060) = 940 lb

Hence quantity of beef jerky produced with 2000 lb of minced meat is 940 lb