Question

13. Persevere in solving problems. The cab company runs a promotion on holidays. The flat rate and the fee per mile are the same, but there is a $1 discount off the fare when the distance traveled is greater than 10 miles. 13 a. How can you modify the expression you wrote in Item 12a to represent a holiday cab fare for a distance greater than 10 miles? Explain. b. Lupe's cab fare on a holiday was $7.50. Did Lupe travel more than 10 miles? Justify your answer. c. How many miles did Lupe travel?

Answer 1

a.

For a distance greater than 10 miles, the cab company offers a $1 discount from the cab fare.

If the normal cab fare is:

C(m)=2+0.5m

Subtract $1 to get the holiday fare:

C(m)=2+0.5m-1

C(m)=1+0.5m

b.

On any normal day the fare for 10 miles is

C(10)=2+0.5*10

C(10)=$7

Any distance greater than 10 miles will result in a fare greater than $7.

During the hollydays she gets a $1 discount, which means that any distance greater than 10 miles will be more than $6

Since she paid $7.50 you can conclude that she traveled more that 10 miles by cab.

c.

Using the expression in a. you can determine the number of miles she traveled by replacing the formula with C=$7.50

C(m)=1+0.5m

7.50=1+0.5m

6.50=0.5m

m=13

She traveled 13 miles.