Gavin took a taxi home from the airport. The taxi fare was $7 plus an additional $0.65 per mile. Gavin gives the driver a $3 tip when he arrives home. If Gavin paid a total of $62.65 with the tip,
what is the distance between the airport and Gavin's house?

Part A: write an equation to determine the distance, m, between the airport and Gavin’s house.

Part B: How many miles are between the airport and Gavin’s house?

a)

We know that:

There is a fixed cost of $7

for each mile, you need to pay $0.65

Then if you take the taxi for "m" miles, the total cost is:

c(m) = $0.65*m + $7

Now we know that Gavin also gives a $3 tip, so we need to add this to the cost:

c(m) = ($0.65*m + $7) + $3 = $0.65*m + $10

c(m) = $0.65*m + $10

Now we know that he paid a total of $62.65

Then:

c(m) = $62.65 =  $0.65*m + $10

This is the equation we need to solve in order to find m, the number of miles between Gavin's house and the airport.

b)

$62.65 =  $0.65*m + $10

We only need to isolate m, we will get:

$62.65 - $10 =   $0.65*m

$52.65/$0.65 =  m = 81

This means that there are 81 miles between the airport and Gavin's house.