CASE STUDY CHALLENGE

Matrices: Orphanage Donation Plan

On her birthday, Prema decides to donate some money to children of an orphanage home.

Orphanage Celebration

Conditions given:

  • • If there are 8 children less, everyone gets ₹ 10 more.
  • • If there are 16 children more, everyone gets ₹ 10 less.

Let the number of children be x and the amount donated to each child be ₹ y.

Answer the following:

(i) Write the system of linear equations in x and y formed by the given situation. [1]
(ii) Write the system of linear equations, obtained in (i) above, in matrix form AX = B. [1]
(iii)

(a) Find the inverse of matrix A.

— OR —

(b) Determine the values of x and y.

 [2]
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