Question

Write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.

Students were asked to bring their favorite fruit to class. 93% of the fruits consisted of bananas, apples, and oranges. If oranges were twice as popular as bananas, and apples were 19 percentage points less popular than bananas, what are the percentages of each individual fruit?

Answer 1

Let the percentage of bananas be x, apples be y and oranges be z.

oranges were twice as popular as bananas, so,

...(ii)

apples were 19 percentage points less popular than bananas

...(iii)

The above system of equations represent the situation.

We know that where A is a matrix.

Thus,

Here,

, since A^-1= adjA^T/|A|

thus,

OR,

  

Thus, the values of x, y and z are 28, 9 and 56 respectively.

ANS:

the percentages of each individual fruits are 28% banana ,9% apple and 56% orange.