Chapter 4.6, Problem 45MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Taxi total. You’re in Manhattan for a job interview. A taxi picks you up from your hotel and takes you x blocks north, then $x/2$ blocks east, then $x+3$ blocks north, then $x/6$ blocks east to your destination. Write an expression in terms of x that gives the total number of blocks traveled. Simplify the expression as much as possible. If the total number of blocks you traveled is 19, determine how many blocks you traveled north between the time you entered the cab and the time the cab first turned east.