Patrick B. answered • 06/15/20

Math and computer tutor/teacher

x is the chicken

y is the corn

z is the milk

40x + 3y + 9z = 35

15x + 16y + 11z = 50.5

100x + 10y + 300z = 370

The solutions are x=1/2, y = 2, z = 1

1/2 serving of chicken, 2 serving of corn, one serving of milk

First, multiplies second equation by 2 to clear the decimal:

40x + 3y + 9z = 35

30x + 32y + 22z = 101

100x + 10y + 300z = 370

Next multiplies the first equation by -3/4 and adds to the second equation:

40x + 3y + 9z = 35

119/4 y + 61/4z = 299/4 <-- 32*4/4 - 9/4 = 119/4 and (88-27)/4=61/4 and (404-105)/4 = 299/4

100x + 10y + 300z = 370

Then multiplies the first equation by -2.5 and adds to the third equation:

40x + 3y + 9z = 35

119/4 y + 61/4z = 299/4

2.5y +277.5z = 282.5

Multiplies the 2nd equation by 4 and the third equation by 2:

40x + 3y + 9z = 35

119y + 61z = 299

** 5y + 555z = 565**

Solves equations 2 and 3 by elimination:

-5( 119y + 61z = 299)

119 ( 5y + 555z = 565)

-595 y + -305z = -1495

595y + 66045 z = 67235

65740 z = 65740

z = 1

The third equation in bold above forces y=2

The original first equation forces x=1/2