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Worked Example 5: Real-World Problem

Plan A: £20 monthly + £0.10 per minute
Plan B: £35 monthly + £0.05 per minute
When do the plans cost the same?

Step 1 Set up equations

Let x = minutes used, y = total cost

Plan A: y = 20 + 0.1x

Plan B: y = 35 + 0.05x

Step 2 Plot both lines

Plan A: starts at (0, 20), gradient 0.1

Plan B: starts at (0, 35), gradient 0.05

Lines will intersect (Plan A rises faster)

Step 3 Find intersection

20 + 0.1x = 35 + 0.05x

0.05x = 15

x = 300 minutes

Plans cost same at 300 minutes (£50)

Step 4 Interpret solution

Below 300 mins: Plan A cheaper

Above 300 mins: Plan B cheaper

At exactly 300 mins: Both cost £50

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