Gauss Jordan equations

Question

Please help me find the correct equations to use gauss Jordan elimination

yiu must makes 500g bowl of food which contains 100g protein and 1200 calories

for each 100g serve the ingredients have the following protein : chicken :30, noodles:12, vegetables :4

for each 100g serve the ingredients have the following calories : chicken:200, noodles:350, vegetables : 30

i have created these equations but the solution does not make sense so think somethings wrong

x +y+z = 500

30x+12y+4z = 100

200x+ 350y+ 30z = 1200

thanks for any help

Answer 1

Let x, y, z be grams of chicken, noodles, and vegetables respectively.

Then x + y + z = 500 (so far so good).

I think here is where you get mixed up with the wording / writing your equations.

If I understand correctly:

1. 100 g of chicken has 30 g of protein and 200 calories, so...
2. 1 g chicken has .3 g protein and 2 cal
3. 100 g of noodles has 12 g of protein and 350 calories, so...
4. 1 g noodles has.12 g of protein and 3.5 cal
5. 100 g of vegetables has 4 g of protein and 30 calories, so...
6. 1 g vegetables has .04 g protein and .3 cal

We need to write two equations: one for protein and one for calories.

For protein:

.3x + .12y + .04z = 100

For calories:

2x + 3.5y + .3z =1,200

Then your three equations are as follows

x + y + z = 500

.3x + .12y + .04z = 100

2x + 3.5y + .3z =1,200

Your mistake seems to have been writing the equations using the amount of protein and calories per 100 g of each food as if it was the info per 1 g, you need to divide the nutrition info by 100 to get calories and protein per gram.

If you solve this you should get:

x = 48,500/189 = 256.61

y = 36,250/189 = 191.80

z = 3,250/63 = 51.59

(I'm assuming you know how to solve, but if you need a hint then start by multiplying equation #2 by 7.5)