Q1.
If a player paid ₹750, how many matches did he play?
Answer
The amount for m matches is the linear polynomial 200 + 50m. Set it equal to 750 — that turns the polynomial into a linear equation.
200 + 50m = 750
50m = 750 − 200 = 550
m = 550 ÷ 50 = 11 matches
50m = 750 − 200 = 550
m = 550 ÷ 50 = 11 matches
Check: 200 + 50 × 11 = 200 + 550 = 750. ✓
Why there is exactly one answer: the joining fee ₹200 is paid once, so of the ₹750 only ₹550 was spent on matches, and each match costs the same ₹50. Because the cost per match never changes, ₹550 can be made up in only one way — 11 matches. A linear polynomial takes each output value exactly once, which is why solving ax + b = c with a ≠ 0 gives a single value of the variable.
Tip: Always separate the one-time part (200) from the repeating part (50m) before dividing. Dividing 750 by 50 straight away would wrongly suggest 15 matches.