Firm A charges £24 up front then £0.60 for each kilometre. Firm B charges £39 up front then £0.35 for each kilometre. At what distance do the two cost the same?

1. Write firm A as cost equals 0.60d plus 24, with d in kilometres and cost in pounds. 2. Write firm B as cost equals 0.35d plus 39. 3. The costs match when 0.60d + 24 = 0.35d + 39. 4. Take 0.35d from both sides to get 0.25d + 24 = 39. 5. Take 24 from both sides to get 0.25d = 15, then divide by 0.25 to get d = 60 kilometres. 6. Check it: firm A costs 24 + 36, which is £60, and firm B costs 39 + 21, which is also £60. 7. Option D comes from dividing the £15 gap in up front charges by 0.30 rather than by 0.25. 8. Option B comes from dividing the £15 gap by 0.20, another wrong gap between the two rates. 9. Option A comes from dividing 24 by 0.60 and ignoring firm B altogether. _Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.2 Modeling with Linear Functions_