System of linear equatins

Question

Four ingrediants, a stir fry favorite, contain a shrimp, pork, beef and chicken with vegetables. the weight of the uncooked ingredients is 20 ounces. The weight of the pork and beef together is the same as the weight of the vegatables. The chicken weights twice as much as the beef. The shrimp beef, and vegatables together weigh 12 ounces. The shrimp and chicken and chicken together weigh 10 ounces. How many ounces are there of each ingrediant?

Answer 1

There are 5 ingredients... we need 5 equations

S+P+B+C+V = 20

P+B = V

C = 2B

S+B+V = 12

S + C = 10

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substitutes C = 2b, which reduces to 4 by 4:

S + P + 3B + V = 20

P + B = V

S + B + V = 12

S + 2B = 10

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substitutes V = P+B, which reduces to 3 by 3:

S + 2P + 4B = 20

S + P + 2B = 12

S + 2B = 10

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subtracts equation 2 MINUS equation 3:

P = 2; reduces to 2 by 2

S + 4b = 16

S + 2b = 10

subtracts these last two equations:

2b = 6

b=3

then v = p +b = 2+3 = 5 and C = 2b = 2*3 = 6

Per the last equation, C+s = 10 ---> S = 4

IN summary

Shrimp weighs 4 oz

chicken weighs 6 oz

pork weighs 2 oz

beef weighs 3 oz

vegetables weigh 5 oz.

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