Zack and Nancy spent two weeks touring Boston, NYC, Philly, and D.C. They paid $

Question

Zack and Nancy spent two weeks touring Boston, NYC, Philly, and D.C. They paid $120, $200, $80, and $1000 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?

A) Answer the question using algebra and logic.

B) Answer the question using the augmented matrix method.

C) Answer the question using the inverse matrix method.

D) Answer the question using Cramer's Rule.

Explanation / Answer

Let B = No. of days in Boston

     N = No. of days in New york

    P = No. of days in Philly

    D = No. of days in DC

It was a 14 Days tour

So, B + P + N + D = 14

N = B + D

N = 3P

allow you to narrow a lot of things down, because you can make substitutions in the first equation based on the other two.

B+P+N+D = 14..............(1)

N = B+D

so, N+N+P = 14

N+N+P = 14

N = 3P

=> N+N+(N/3) = 14

This last equation is in one variable, so we solve for N to get ;

3N + 3N + N = 42

7N = 42

=> N = 6

It immediately follows from

N = 3P

that

P = N/3 = 6/3 = 2

Hence P = 2

Now we need B and D. so, plug N and P in B+P+N+D = 14, WE GET:

B + 2 + 6 + D = 14

B + D + 8 = 14

so, B + D = 6

120B + 200N + 80P + 1000D = 2020

solve these equations we get:

B = 3 , N =6, P = 2, D = 3

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