A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹50 and for each table is ₹200. The school spends ₹30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding stimulus
Model Answer
Let number of chairs = x, number of tables = y.
(i) The pair of linear equations:
$$x + y = 300$$
$$50x + 200y = 30000$$
(ii) From equation (i): x = 300 − y
Substituting in equation (ii):
$$50(300 - y) + 200y = 30000$$
$$15000 - 50y + 200y = 30000$$
$$150y = 15000 \Rightarrow y = 100$$
$$x = 300 - 100 = 200$$
∴ Number of chairs = 200, Number of tables = 100
(iii) If no chairs are rented (x = 0):
$$200y = 30000 \Rightarrow y = 150$$
∴ Maximum number of tables = 150
Source: Pair of Linear Equations in Two Variables
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Explanation
- (i) Simply translate both conditions (total items and total cost) into equations — examiners want both equations clearly stated.
- (ii) Use substitution method; show each step clearly. State the final answer in words.
- (iii) Put x = 0 directly in the cost equation — this is a straightforward 1-mark application. Don't overthink it.