Formulate but do not solve the problem.

Joan and Dick spent 2 weeks (14 nights) touring four cities on the East Coast: Boston, New York, Philadelphia, and Washington. They paid$210,$500,$190, and$150per night for lodging in each city, respectively, and their total hotel bill came to$4520. The number of days they spent in New York was the same as the total number of days they spent in Boston and Washington, and the couple spent 3 times as many days in New York as they did in Philadelphia. How many days did Joan and Dick stay in each city? (Letx,y,z, andwdenote the numbers of days spent in Boston, New York, Philadelphia, and Washington, D.C., respectively.)

=14

=4520

=x+w

=3z