I need help with this question: Write a system of linear equations for this prob
ID: 3185818 • Letter: I
Question
I need help with this question:
Write a system of linear equations for this problem and solve the system using Gaussian elimination method. Show your work completely.
The accompanying table shows the percentage of U.S. Recommended Daily Allowances(RDA) for phosphorus(P), magnesium(Mg), and Calcium(Ca) in one ounce of three breakfast cereals (without milk).
If Hulk Hogan got 98% of the RDA of phosphorus, 84% of the RDA of magnesium, and 38% of the RDA of calcium by eating a large bowl of each(without milk), then how many ounces of each cereal did he eat?
Phosphorus Magnesium Calsium Kix 4% 2% 4% Quick Oats 10% 10% 0% Muesli 8% 8% 2%Explanation / Answer
Let Hulk Hogan eat x oz. of Kix, y oz. of Quick Oats and z oz. of Muesli. Then 4x+10y+8z = 98 or, 2x+5y+4z = 49…(1). Also, 2x+10y+8z = 84 or, x+5y+4z = 42…(2) and 4x+2z = 38 or, 2x+z = 19…(3).
The augmented matrix of this linear system is A =
2
5
4
49
1
5
4
42
2
0
1
19
To solve this linear system, we have to reduce A to its RREF, which is
1
0
0
7
0
1
0
3
0
0
1
5
Thus, x = 7,y = 3 and z= 5.
Hence, Hulk Hogan ate 7 oz. of Kix, 3 oz. of Quick Oats and 5 oz. of Muesli.
2
5
4
49
1
5
4
42
2
0
1
19