SOLUTION: Jack and Jill spent two weeks touring Boston, New York, Philly, and Washington. They paid $120, $200, $80, and $100 per night respectively. Their total bill was 2020. The number of

Question 1110556: Jack and Jill spent two weeks touring Boston, New York, Philly, and Washington. They paid $120, $200, $80, and $100 per night respectively. Their total bill was 2020. The number of days spent in NYC was the same as the sum of the days spent in Boston and DC. They spent three times as many days in NYC as they did in Philly. How many days did they stay in each city?
It says to answer the question using a 4x4 system of equations. I can't think of how to even start this :/
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) the total number of days was 14 (two weeks)
(2) the total cost for lodging was $2020
(3) the number of days spent in NYC was the same as the sum of the days spent in Boston and DC
(4) they spent three times as many days in NYC as they did in Philly

Four equations, four unknowns.

With 4 equations in 4 variables, there are always many different ways to find the answer. Here is what I did....

I separated the 120B into 100B+20B so I could use equation (3)

(5)

With this equation (5), knowing that B, N, P, and W are whole numbers less than 14, there is only one possible value for P: P=2. Then it follows immediately that B=3. Equation (4) then gives N=6; and equation (1) then gives W=3.

Answer: Philly 2, Boston 3, New York 6, Washington DC 3.
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