The cost of a journey is given by the linear function C(d) = 100 + 60d, where C indicates total cost in rupees and d the distance travelled in km.
What is the cost for travelling 15 km? For how many kilometres will the cost of the journey be ₹700?

Step-by-step solution

Idea: The first part is an input (find the output). The second part gives the output; set up the equation and solve for the input.

1. C(15) = 100 + 60 × 15 = 100 + 900 = ₹1000.1 mark
2. 100 + 60d = 700 ⇒ 60d = 600 ⇒ d = 10 km.1 mark

Check: C(10) = 100 + 600 = 700 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Working out 100 + 60 × 15 as 160 × 15 = 2400. Multiply first: 60 × 15 = 900, then add 100.
• Solving 100 + 60d = 700 as d = 700 ÷ 60 ≈ 11.7, forgetting the fixed ₹100.
• Mixing up the two questions: giving a distance for the first and a cost for the second.

How this can come in the exam

Try one yourself

Using C(d) = 100 + 60d, find the cost for 8 km and the distance for which the cost is ₹1300.

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