Question 1110439
 Jack and Jill spent two weeks touring Boston, New York City, Philadelphia, and Washington D.C.
let b, n, p, and w = the no. of days in each season, write an equation for each statement
:
 They paid $120,$200,$80, and $100 per night respectively.
 Their total bill was $2020.
120b + 200n + 80p + 100w = 2020
Simplify, divide by 20
6b + 10n + 4p + 5w = 201
:
 The number of days spent in NYC was the same as the sum of the days spent in Boston and D.C.
n = b + w
or
b = n - w
:
 They spent three times as many days in NYC as they did in Philly.
n = 3p
or
p = {{{n/3}}}
:
a) answer question using a combination of algebra and logic.
Substitute in the 1st equation, for b & p
6(n-w) + 10n + 4({{{n/3}}} + 5w = 101
get rid of the fraction, multiply thru b 3
18(n-w) + 30n + 4n + 15w = 303
18n - 18w + 30n + 4n + 15w = 303
combine like terms
52n - 3w = 303
have 4 unknowns and only 3 equations, but we know they have to be integers
Write an equation we can enter into a graphing calc
3w = 52n - 303
w = {{{(52n-303)/3}}}
w = {{{52/3}}}n - 101
table reveals only one integer solution that makes sense
n = 6, w = 3
therefore
p = 6/3 = 2 days
b = 6 - 3 = 3 days
:
How many days did they stay in each city? 
Boston 3 days, New York 6 days, Philly 2 days and Wash 3 days
see if that works
120(3) + 200(6) + 2(80) + 100(3) = 2020
:
 b) answer the question again using a 4x4 system of equations.
I don't know either,  how you could do this with a 4 by 4 matrix