KBAT Problems
KBAT Problem: Choosing Between Two Data Plans
An original multi-step KBAT problem that models two mobile data plans as linear cost functions, finds the break-even usage, and turns the maths into a real recommendation.
The problem
Two mobile data plans are on offer. Plan A costs RM30 a month and includes 5 GB of data; each extra GB beyond that costs RM2.
Plan B costs RM45 a month and includes 12 GB of data; each extra GB beyond that costs RM1.50. For a user whose monthly data usage is always above 12 GB, which plan should they choose, and at what usage does it not matter?
Full worked solution
- Understand and set up: Let x be the estimated data usage in GB, where x > 12 so both plans have used up their included data. Plan A costs CA = 30 + 2(x − 5) = 2x + 20. Plan B costs CB = 45 + 1.5(x − 12) = 1.5x + 27.
- Plan and solve: The two plans cost the same when CA = CB, so 2x + 20 = 1.5x + 27. Subtracting 1.5x from both sides gives 0.5x + 20 = 27, so 0.5x = 7 and x = 14.
- Execute, check and decide: At x = 14, CA = 2(14) + 20 = RM48 and CB = 1.5(14) + 27 = RM48, confirming the break-even point. Since Plan A's cost rises faster (gradient 2 against 1.5), Plan A is cheaper below 14 GB and Plan B is cheaper above 14 GB; at exactly 14 GB the two cost the same.
Mark-scheme keywords
- Correct cost expression for Plan A: CA = 2x + 20 (or an equivalent unsimplified form).
- Correct cost expression for Plan B: CB = 1.5x + 27 (or an equivalent unsimplified form).
- Equating the two expressions and solving correctly for x = 14.
- Stating the break-even cost, RM48, not just the value of x.
- A clear final decision: Plan A for usage below 14 GB, Plan B for usage above 14 GB.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
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