Solve a linear system in context — break-even point
Solve a linear system algebraically to find where two plans (each a fixed fee plus a rate) cost the same. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Two car rental options charge differently. Plan A costs $8.00 flat plus $0.80 per km. Plan B costs $20.60 flat plus $0.10 per km. After how many kilometres do the two plans cost the same?
Cost = rate · x + fee
Answer: 18
See one solved, step by step
Two car rental options charge differently. Plan A costs $17.00 flat plus $0.30 per km. Plan B costs $28.40 flat plus $0.15 per km. After how many kilometres do the two plans cost the same?
Cost = rate · x + fee
📘 Worked solution
1Plan A: C = 0.3x + 17 Plan B: C = 0.15x + 28.4Write a cost equation for each plan, where x is the number of kilometres.
20.3x + 17 = 0.15x + 28.4At the break-even point the two plans cost the same amount, so set the two expressions equal to each other.
3(0.3 - 0.15)x = 28.4 - 17Move the x-terms to one side and the numbers to the other.
4x = 11.4 / 0.15 = 76Divide to solve for x.
5After 76 kilometres, both plans cost the same.That's the break-even point.
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