# Math Help - problem solving

1. ## problem solving

I have another problem i cound't figure how to start.

problem:

Jack and Jill spent two weeks (14 nights) touring boston, new york city, philadelphia, and washington d.c. they paid $120,$200, $80, and$100 per night respectively. their total bill was $2020. the number of days spend in NYC was the same as the total number days spent in boston and d.c. They spent 3 nights as many days in NYC as they did in philly. How many days did they stay in each city? please help. thanks! 2. Originally Posted by Anemori I have another problem i cound't figure how to start. problem: Jack and Jill spent two weeks (14 nights) touring boston, new york city, philadelphia, and washington d.c. they paid$120, $200,$80, and $100 per night respectively. their total bill was$2020. the number of days spend in NYC was the same as the total number days spent in boston and d.c. They spent 3 nights as many days in NYC as they did in philly. How many days did they stay in each city?
$b,n,p,w$ stand for the number of days/nights each city Jack and Jill stayed in.

Here's some equations to work with

$120b +200n+80p+100w=2020$

Can it be assumed the number of days = the number of nights? If so also

$n=b+w$

3. 120b +200n+80p+100w=2020

b=3
n=6
p=2
w=3

I plugged those numbers and i got it right...

120(3)+200(6)+80(2)+100(3)=2020

If I didn't know those numbers and i want to use matrices to find those numbers, what should i do?