Q1.
Example 13: Can you give a real-life situation that can be modelled as the equation, 100x + 75 = 250?
Answer
Yes. Read the numbers as rupees: ₹75 is a fixed charge, x is the cost of one item, 100 is the number of items, and ₹250 is the total bill.
100x + 75 = 250
100x = 250 − 75 = 175
x = 175 ÷ 100 = ₹1.75 per item
100x = 250 − 75 = 175
x = 175 ÷ 100 = ₹1.75 per item
Some situations that fit:
- A shop sells 100 pencils at ₹x each and charges ₹75 for packing. The bill is ₹250. What does one pencil cost?
- A tent for a school function is booked for 100 chairs at ₹x a chair, with a fixed ₹75 for transport, and the total is ₹250.
- An internet plan costs ₹75 a month plus ₹x for each of 100 units used; the bill comes to ₹250.
Why it happens: the shape of the equation tells you what story fits. A term with the unknown in it is something that changes with the quantity — a rate. A plain number added to it is something fixed. The number on the other side is the total. Madhubanti's party, the taxi fare and the savings problems in this chapter all share that shape.
Check it yourself: 100 × 1.75 = 175, and 175 + 75 = 250. ✓