Question

1. 110 ice creams of different flavors are purchased weekly in a student residence: vanilla, passion fruit, and coconut. The budget for this purchase is 540 euros and the price of each ice cream is 4 euros for vanilla, 5 euros for passion fruit and 6 euros for coconut. Once the students' tastes are known, it is known that between 20% passion fruit and coconut ice cream, vanilla must be purchased. to. A. Solve using a system of linear equations to calculate how many ice creams of each flavor are bought per week. b. Solve, using the Gauss Jordan Method

Answer 1

Let, x, y, z denote the no of vanilla, passion fruit and coconut ice creams bought per week.

Then, according to the question, the given equations are:-

..................total number of ice creams.....1

..............price of each ice cream and total budget......2

............taste of students........3

Now, solving this as a system of linear equations, putting the value of eq3 in eq1 and eq2 we get:

...4

...5

Multiplying eq4 by 5 and subtracting eq5 from it, we get:-

From this, we get:-

Hence, 35 vanilla, 50 passion fruit and 25 coconut ice creams are ordered each week.

Now, we solve the same equations using Gauss_Jordan elimination. The augmented matrix of the given equation is

Finding the pivot in the first column and eliminating the other entries by R₂=R₂-4R₁ and R₃=R₃-R1, we get:-

Similarly, R₁=R₁-R₂ and R₃=R₃+1.2R₂ gives us:-

Dividing R₃by 0.4 we get:-

Finally, eliminating the rest of the column using R₁=R₁+R₃and R₂=R₂-2R₃we get

Thus, our solution is given by x=35, y=50, z=25. Which matches with our previous solution.