Question

Three schools $A,\;B$ and $C$ organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold handmade fans, mats and plates from recycled material at a cost of $Rs.25\;,\;Rs.100$ and $Rs.50$ each. The number of articles sold are given below :

Articles	School $A$	School $B$	School $C$
Hand –fans	$40$	$25$	$35$
Mats	$50$	$40$	$50$
Plates	$20$	$30$	$40$

Find the fund collected by each school separately by selling the above articles. Also, find the total funds collected for the purpose.

Answer 1

Hint: In this question we have to follow the steps for multiplying two matrices i.e. first the number of rows in $1st$ one equals the number of columns in $2nd$ one, second is multiplying the elements of each row of the first matrix by the elements of each column in the second matrix and now third and last step is to add the products.

Complete step-by-step answer:
According to the question we have ,

Articles	School $A$	School $B$	School $C$	Cost (per article)
Hand –fans	$40$	$25$	$35$	$25$
Mats	$50$	$40$	$50$	$100$
Plates	$20$	$30$	$40$	$50$

So, now we have to calculate the total fund collected by School $A\;,\;B$ and $C$. Hence, the funds collected by each school can be obtained by matrix multiplication, we get
\[\left[ {\begin{array}{*{20}{c}}
  {40}&{50}&{20} \\
  {25}&{40}&{30} \\
  {35}&{50}&{40}
 \end{array}} \right] \]\[\left[ {\begin{array} \
  25 \\
  100 \\
  50 \\
 \end{array}} \right] \] = \[\left[ {\begin{array} \
  7000 \\
  6125 \\
  7875 \\
 \end{array}} \right] \]
Hence , Funds collected by School $A$$ = 7000$
Funds collected by School $B = 6125$
Funds collected by School $C = 7875$
Hence , Total funds collected $ = 7000 + 6125 + 7875 = 21000$

Note: In such types of questions the concept of conformance for multiplication of matrices applies that is for matrix multiplication to work, the columns of the second matrix have to have the same number of entries as do the rows of the first matrix.