# Thread: System of Linear Equations

1. ## System of Linear Equations

A man is preparing a meal consisting of foods A,B,C.Each ounce of food A contains 2 units of protein ,3 units of fat & 4 units of carbohydrates.Each ounce of food B contains 3,2,1 units of protein ,fats and carbohydrates resp. And each ounce of food C contains 3,3,2 units of P, F and C.H resp.

If the meal must provide exactly 25 units of P, 24 units of F and 21 units of C.H, thenhow many ounces of each food should be used,by taking the required units of P,F and C.H as x,y,z.

Thanks

2. Originally Posted by abds
A man is preparing a meal consisting of foods A,B,C.Each ounce of food A contains 2 units of protein ,3 units of fat & 4 units of carbohydrates.Each ounce of food B contains 3,2,1 units of protein ,fats and carbohydrates resp. And each ounce of food C contains 3,3,2 units of P, F and C.H resp.

If the meal must provide exactly 25 units of P, 24 units of F and 21 units of C.H, thenhow many ounces of each food should be used,by taking the required units of P,F and C.H as x,y,z.

Thanks
let x be the amount of A needed, y the amount of B needed, and z be the amount of C needed.

for Protein:
2x + 3y + 3z = 25 ............(1)

for Fat:
3x + 2y + 3z = 24 ............(2)

for Carbs:

4x + y + 2z = 21 ..............(3)

you have three equations with three unknowns. solve the system simultaneously

3. Originally Posted by abds
A man is preparing a meal consisting of foods A,B,C.Each ounce of food A contains 2 units of protein ,3 units of fat & 4 units of carbohydrates.Each ounce of food B contains 3,2,1 units of protein ,fats and carbohydrates resp. And each ounce of food C contains 3,3,2 units of P, F and C.H resp.

If the meal must provide exactly 25 units of P, 24 units of F and 21 units of C.H, thenhow many ounces of each food should be used,by taking the required units of P,F and C.H as x,y,z.

Thanks
let food A be x ounce, B be y and C be z

so 2x + 3y + 3z = 25
3x + 2y + 3z = 24
4x + y + 2z = 21

Now solve these equation for x,y and z