Je lneels cab fares in NYC. Jack and Jill spent two weeks touring Boston, New Yo

Question

Je lneels cab fares in NYC. Jack and Jill spent two weeks 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 spent in NYC was the same as the sum of the days spent in Boston and D.C. They spent three times as many days in NYC as they did in Philly. How many days did they stay in each city? Anawer the question using a combinatin of lgetira and logic b) Answer the question again using a 4 x 4 system of equations. (Turn Over)

Explanation / Answer

4 x 4 system means, 4 variables and 4 equations.

Only part (b) is requested in the question -

Let the no. of nights spent in Boston, New York, Philadelphia and Washington are B, N, P, W respectively -

bill from B night of Boston = 120B, similarly for other cities : 200N, 80P and 100W

Total bill = 2020 = 120B + 200N + 80P + 100W ....(1)

Numbers of days psent in NYC is same as sum of the days in Boston and Washington D.C.

N = B + W

B - N + 0P + W = 0...(2)

Three times as many days in NYC as in Philly

N = 3P

0B + N - 3P + 0W = 0...(3)

2 weeks spent in the 4 cities, so total number of days should be 14.

B + N + P + W = 14 ...(4)

120B + 200N + 80P + 100W = 2020....(1)

B - N + 0P + W = 0...(2)

0B + N - 3P + 0W = 0...(3)

B + N + P + W = 14 ...(4)

solve using substitution method

put P = N/3 (from eq 3) and B = N - W (from eq 2) in eq1 and eq4 and get the equations in the form N and W

eq4: N - W + N + N/3 + W = 14

7N/3 = 14

N = 6

Put N in eq (1) to get W = 3

use the P = N/3 and B = N - W ,

final answers B = 3, N = 6, P = 2, W = 3

please upvote the answer.

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