Algebra question

Question

Let’s say each once of macaroni contains 4 grams of protein and 3 grams of fat, and each ounce of salmon contains 6 grams of protein and 2 grams of fat. How many ounces of each food should be used to prepare a lunch containing 46 grams of protein and 27 grams of fat.

Answer 1

1st equation:

4M + 6S = 46

2M + 3S = 23

 

2nd equation:

3M + 2S = 27

 

 

2M + 3S = 23

3M + 2S = 27

 

Multiplies 1st equation by 3 and 2nd equation by -2

 

6M + 9S = 69

-6M + -4S = -54

 

5S = 15

S=3

 

3 grams of salmon

 

 

Plugs into 1st equation:

2M + 3(3) = 23

2M + 9 = 23

2M = 14

M=7

7 grams of macaroni

 

7 grams of macaroni

3 grams of salmon.

 

CHECK:

 

  7x4 + 3x6 = 28+18 = 46

 7x3 + 3x2  = 21+6 = 27

Yes, the answers are correct