A dietician in a hospital is to arrange a special diet compo

A dietician in a hospital is to arrange a special diet composed of three basic foods. The diet is to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitamin A. The number of units per ounce of each special ingredient for each of the foods is indicated in the table: How many ounces of each food must be used to meet the requirements?

Solution

xA +yB+zC=340

xA + yB+zC=180

xA+yB+zC=220

30x+10y+20z=340

10x+10y+20z=180

10x++30y+20z=220

SUBTRACTING 1 EQN FROM EQMLN2 we have ,

20x=160, x=8.

SUBTRACTING EQN 1 from EQN 3,

20x =20y. So y =8. Putting this in EQN 1

240+80+20z=340, z=1.

So, A B C are to be ordered in quantities 8 8 1 respectively