# Taxi Problem

More Options: Make a Folding Card

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#### Storyboard Text

• 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!