Taxi Problem

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  • Taxi driver, how much will it cost me to ride into downtown St.Louis?
  • Taxi Driver: For the first 6 miles it will cost $3.00 a mile, after 6 miles it will cost you $5.25 a mile. To figure out how much it will cost you, create a linear equation to solve how much money you'll pay depending on how far I drive you.
  • I know that the beginning of the equation will begin with c=5.25d. c will represent the cost and d will represent the number of miles. The last part of my equation will be -13.50 because of the cost increase I will over pay by $13.50.
  • The equation is c= 5.25d - 13.50!
  • Good! Now how much will it cost you to go 10 miles? How about if you only had $20, how many miles could you go?
  • If I were to travel 10 miles it would cost me $39. This is so because 5.25 x 10 = 52.50. Then 52.50 - 13.50 = 39.
  • The staring point would be $13.50, while the rate of change would be $5.25 because the cost increases by $5.25 every mile.
  • Taxi Driver: Right! Now if you only had $20 the farthest you would be able to go is about 6 miles which is only $18. So, what is the cost-intercept, or the starting point? How about the slope, or rate of change?
  • So, how far am I taking you downtown?
  • Well I only have $50. How many miles can I go? If 10 miles is $39, and 11 miles is $44.25. Then 5.25 x 12 = 63. 63 - 13.50 = 49.50. So I can go 12 miles!
  • That'll be $49.50!
  • Take me 12 miles downtown please!
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