SOLUTION: Please help me solve this..: Food A has 560 calories per pound and 80 units of vitamins per pound, Food B has a 240 calories per pound and 400 units of vitamins per pound, and food

Question 997500: Please help me solve this..: Food A has 560 calories per pound and 80 units of vitamins per pound, Food B has a 240 calories per pound and 400 units of vitamins per pound, and food C has 480 calories per pound and 160 units of vitamins per pound. It is desired to have a 10-lb mixture of foods A,B,and C to contain a total of 2000 calories and 1200 units of vitamins. Show that these requirements lead to an inconsistent system of equations, and therefore the mixture in not possible.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = number of pounds of A.
let b = number of pounds of B.
let c = number of pounds of C.

you get 3 equations that need to be solved simultaneoulsy.

they are:

a + b + c = 10 = total number of pounds.
560 a + 240b + 480c = 2000 = total number of calories.
80a + 400b + 160c = 1200 = total units of vitamins.

the calculartions are shown below:

in 1 we write the equations as shown above.

in 2 we multiply the first equation by 560 and subtract the second equation from that to get 320b + 80c = 3600

in 3 we multiply the first equation by 80 and subtract the first equation from the third equation to get 320b + 80c = 400

in 4 we subtract 320b + 80c = 400 from 320b + 80c = 3600 to get 0 + 0 = 3200

we are left with 0 = 3200 which is not true and so there is no common solution to these 3 equations.

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