A school is organising its Annual Day function and plans to decorate every chair with a ribbon and…
A school is organising its Annual Day function and plans to decorate every chair with a ribbon and every table with a cover. There are 150 chairs and 20 tables, all of which need decorations. Company A charges ₹ 12 per chair ribbon and ₹ 180 per table cover. Company B charges ₹ 10 per chair ribbon and ₹ 200 per table cover.
By setting up one matrix equation that include both companies, compare the overall prices that would be charged by the two companies.
Answer
Answer
AIWritten by AI - it can contain mistakes.
Let the quantity matrix be $Q = \begin{bmatrix} 150 & 20 \end{bmatrix}$, representing 150 chair ribbons and 20 table covers.
Let the price matrix for the two companies be $P = \begin{bmatrix} 12 & 10 \\ 180 & 200 \end{bmatrix}$, where column 1 corresponds to Company A and column 2 corresponds to Company B.
The total cost matrix is given by $C = QP$:
$C = \begin{bmatrix} 150 & 20 \end{bmatrix} \begin{bmatrix} 12 & 10 \\ 180 & 200 \end{bmatrix}$
$= \begin{bmatrix} 150(12) + 20(180) & 150(10) + 20(200) \end{bmatrix}$
$= \begin{bmatrix} 1800 + 3600 & 1500 + 4000 \end{bmatrix}$
$= \begin{bmatrix} 5400 & 5500 \end{bmatrix}$.
Company A charges ₹ 5,400 and Company B charges ₹ 5,500.
Comparing the overall prices, Company A is cheaper by ₹ 100.
From ISC 2027 Specimen Mathematics Paper 1, question 13(ii).