A chess club charges a joining fee of ₹200 plus ₹50 for every match played. The following table shows the amount a player will have to pay as the number of matches varies.

Step-by-step solution

Idea: The joining fee is fixed; only the match charge grows. For m matches the match charge is 50 × m.

1. Amount = 200 + 50 × (number of matches):

   Number of matches played	1	2	3	4	5	…	m
   Amount paid (₹)	250	300	350	400	450	…	200 + 50m

   1 mark
2. So for m matches the total cost is ₹(200 + 50m). The highest power of m is 1, so 200 + 50m is a linear polynomial in m.½ mark
3. Each extra match adds the same ₹50 (250, 300, 350, …). This constant increase is what makes the pattern linear.½ mark

Check: For 4 matches: 200 + 50 × 4 = 400, which matches the table ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing 250m (charging the joining fee for every match). The ₹200 is paid only once.
• Writing 200m + 50. Here the fixed amount and the per-match amount have been swapped.
• Forgetting the joining fee and writing 50m.

How this can come in the exam

Try one yourself

A taxi app charges ₹60 booking fee and ₹18 per km. Write the fare for k km and find it for 12 km.

More questions like this

• A chess club charges a joining fee of ₹200 plus ₹50 for every match played. If a player paid ₹750, how many matches did he play?
• The sum of two numbers is 64. One of the numbers is 10 more than the other. What are the two numbers?
• We have learnt that to evaluate the value of an algebraic expression, we substitute a value of the variable in the given expression. Consider the example where the wire is bent to form a rectangle. Here, the area of the rectangle, 10x − x², is a function of x. Can you interpret this as an input-output process? What value does the expression take when x = 6 cm?
• Find the value of the linear polynomial 5x − 3 if:
• Find the value of the quadratic polynomial 7s² − 4s + 6 if:

All Linear polynomials questions · All maths questions