**Case Study - 1**

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 food supplier. It fin

Question

**Case Study - 1**

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 food supplier. It finds that rent for each chair is Rs 10 and for each table is Rs 200. The school spends Rs 30,000 for renting the total number of items (chairs and tables) rented are 300.

If the school rents '$x$' chairs and '$y$' tables, answer the following questions:

(i) Write down the pair of linear equations representing the given information.

(ii) (a) Find the number of chairs and number of tables rented by the school.

**OR**

(ii) (b) If the school wants to spend a maximum of Rs 27,000 on 300 items (tables and chairs), then find the number of chairs and tables it can rent.

(iii) What is maximum number of tables that can be rented in Rs 30,000 if no chairs are rented?

Accepted Answer

Step 1: (i) $x + y = 300$
and $50x + 200y = 30000$ or $x + 4y = 600$
Step 2: (ii)(a) Solving the equations, we get
$x + y = 300$ and $x + 4y = 600$
Subtracting: $3y = 300 \Rightarrow y = 100$ and $x = 200$.
$	herefore$ Number of chairs and tables rented by the school are 200 and 100 respectively.

**OR**

(ii)(b) $x + y = 300$ and $50x + 200y = 27000$ or $x + 4y = 540$.
Solving: $3y = 240 \Rightarrow y = 80$ and $x = 220$.
$	herefore$ Number of chairs and tables rented are 220 and 80 respectively.
Step 3: (iii) Number of tables $= \frac{30000}{200} = 150$.
$	herefore$ Maximum number of tables that can be rented is 150 if no chairs are rented.

Question

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