Question

Joan and Dick spent 2 weeks (14 nights) touring four cities on the East Coast–Boston, New York,
Philadelphia, and Washington. They paid $120, $200, $80, and $100 per night for lodging in each city,
respectively, and their hotel bill came to $2020. 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

Answer 1

Let the number of days spent by couple in Philadelphia be x, and in Washington be y,

Number of days spent by couple in New York = 3x

Number of days spent by couple in Boston = 3x - y

We get 2-equations. They are-

x+y+3x+3x-y=14 ...(1)

7x=14

x=2

And the second equation is-

120(3x-y) + 200(3x) + 80(x) + 100y = 2020 ...(2)

1040x-20y = 2020

1040(2) - 20y = 2020

20y = 60

y=3

Days spent in New York=6 days

Days spent in Washington=3 days

Days spent in Philadelphia=2 days

Days spent in Boston=3 days