Application of linaer system on DIet.

1. Group 6
Name/NIM :
1. Hanifa Sintriani/1711440003
2. Meutiah Nahrisyah/1711441014
Applications of Linear Systems
“DIET”
An individual wantsto use milk and orange juice to increase the amount of calcium and vitamin
A in her daily diet. An ounce of milk contains 38 milligrams of calcium and 56 micrograms of vitamin
A. An ounce of orange juice contains 5 milligrams of calcium and 60 micrograms of vitamin A. How
many ounces of milk and orange juice should she drink each day to povide exactly 550 milligrams of
calcium and 1200 micrograms of vitamin A?
Solution :
First we define the relevant variables :
𝑥 = number of ounces of milk
𝑦 = number of ounces of orange juice
Next we summarize the given informations in a table. It is convenient to organize the tables so that the
quantities represented by the variables correspond to columns in the table (rather than to rows), as
shown.
Milk Orange Juice Total Needed
Calcium (𝒎𝒈) 38 5 550
Vitamin A (𝝁𝒈) 56 60 1200
Now we use the information in the table to form equations involving 𝑥 and 𝑦 :
(
𝐶𝑎𝑙𝑐𝑖𝑢𝑚 𝑖𝑛 𝑥 𝑜𝑧
𝑜𝑓 𝑚𝑖𝑙𝑘
) + (
𝐶𝑎𝑙𝑐𝑖𝑢𝑚 𝑖𝑛𝑦 𝑜𝑧
𝑜𝑓 𝑜𝑟𝑎𝑛𝑔𝑒 𝑗𝑢𝑖𝑐𝑒
) = (
𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑙𝑐𝑖𝑢𝑚
𝑛𝑒𝑒𝑑𝑒𝑑 ( 𝑚𝑔)
)
38𝑥 + 5𝑦 = 550
(
𝑉𝑖𝑡𝑎𝑚𝑖𝑛 𝐴 𝑖𝑛 𝑥 𝑜𝑧
𝑜𝑓 𝑚𝑖𝑙𝑘
) + (
𝑉𝑖𝑡𝑎𝑚𝑖𝑛 𝐴 𝑖𝑛 𝑦 𝑖𝑧
𝑜𝑓 𝑜𝑟𝑎𝑛𝑔𝑒 𝑗𝑢𝑖𝑐𝑒
) = (
𝑇𝑜𝑡𝑎𝑙 𝑣𝑖𝑡𝑎𝑚𝑖𝑛 𝐴
𝑛𝑒𝑒𝑑𝑒𝑑 (𝜇𝑔)
)
56𝑥 + 60𝑦 = 1200
 Solve first equation for 𝑦 :
38𝑥 + 5𝑦 = 550
𝑦 = 110 − 7.6𝑥
 Subtitute for 𝑦 in second equation :
56𝑥 + 60(110 − 7.6𝑥) = 1200
56𝑥 + 6600 − 456𝑥 = 1200
−400𝑥 = −5400

2. 𝑥 = 13.5
 Subtitute 𝑥 in 𝑦 = 110 − 7.6𝑥
𝑦 = 110 − 7.6(13.5)
𝑦 = 7.4
So, we can conlude that drinking 13.5 ounces of milk and 7.4 ounces of orange juice each day will
provide the required amount of calcium and vitamin A.
Check :
38𝑥 + 5𝑦 = 550
38(13.5) + 5(7.4) ≟ 550
500 = 500∎
56𝑥 + 60𝑦 = 1200
56(13.5) + 60(7.4) ≟ 1200
1200 = 1200∎