.DETERMINE HOW MANY OUNCES OF MILK AND ORANGE JUICE ANITA SHOULD DRINK EACH DAY TO PROVIDE EXACTLY 550MILLIGRAMS OF CALCIUM AND 1200MICROGRAMS OF VITAMIN A BY C

Question

Anita wants to use milk and orange juice to increase the amount of calcium and vitamin A IN HER DAILY DIET.aN OUNCE OF ORANGE OF MILK CONTAINS 38 MILLIGRAMS OF CALCIUM AND 56MICROGRAMS OF VITAMIN A.AN OUNCE OF ORANGE JUICE CONTAINS 5MILLIGRAMS OF CALCIUM AND 60MICROGRAMS OF VITAMIN A.DETERMINE HOW MANY OUNCES OF MILK AND ORANGE JUICE ANITA SHOULD DRINK EACH DAY TO PROVIDE EXACTLY 550MILLIGRAMS OF CALCIUM AND 1200MICROGRAMS OF VITAMIN A BY CRAMMERS RULE

Answer 1

First, set up a system of equations:

let x = ounces of milk and y = ounces of orange juice

38x + 5y = 550

56x + 60y = 1200

 

In Matrix format:

[38   5] *[x] = [550 ]

[56 60]   [y]    [1200]

 

If 38*60 - 5*56 is nonzero, then we can use determinants  to solve for x and y using Cramer's rule:

x = det [550    5] / det [38    5]

           [1200 60]         [56  60]

 

x = (550*60 - 1200*5) / (38*60 - 5*56) = 13.5

 

y = det [38   550] / det [38    5]
            [56 1200]         [56  60]

 

 
x = (38*1200 - 550*56) / (38*60 - 5*56) = 7.4