Mario took a 17 day trip around the U.S. He visited Boston, Miami, Philadelphia and New York. In Boston he spent $200 per day, in Miami $225 per day, in Philadelphia $175 per day and in New York he spent $150 a day for a total of $3400. The number of days he spent in Miami was one less than the total number of days in the other three cities combined. The number of days in Philadelphia was twice the number of days in New York.How many days did Mario spend in each city?

b+m+p+n=17

200b+225m+175p+150n=3400
m = b+p+n-1
p = 2n

Now just solve for the 4 unknowns.

To solve this problem, let's set up a system of equations using the given information.

Let:
- B = number of days spent in Boston
- M = number of days spent in Miami
- P = number of days spent in Philadelphia
- N = number of days spent in New York

We are given the following information:

1. Mario took a 17-day trip around the U.S.
This can be expressed as: B + M + P + N = 17 (Equation 1)

2. In Boston, he spent $200 per day.
This can be expressed as: B * $200

3. In Miami, he spent $225 per day.
This can be expressed as: M * $225

4. In Philadelphia, he spent $175 per day.
This can be expressed as: P * $175

5. In New York, he spent $150 per day.
This can be expressed as: N * $150

We are also given the total amount spent, which is $3400.
This can be expressed as: (B * $200) + (M * $225) + (P * $175) + (N * $150) = $3400 (Equation 2)

Additionally, we have the following information:

6. The number of days spent in Miami was one less than the total number of days in the other three cities combined.
This can be expressed as: M = (B + P + N) - 1 (Equation 3)

7. The number of days in Philadelphia was twice the number of days in New York.
This can be expressed as: P = 2N (Equation 4)

Now, we can solve this system of equations simultaneously to find the values of B, M, P, and N.

Let's start by substituting Equations 3 and 4 into Equation 1:

B + M + P + N = 17
B + ((B + P + N) - 1) + P + N = 17
2B + 2P + 2N - 1 = 17
2B + 2(2N) + 2N - 1 = 17 (Substituting P = 2N)
2B + 4N + 2N - 1 = 17
2B + 6N - 1 = 17
2B + 6N = 18 (Adding 1 to both sides)

Now, let's substitute the expressions for the amount spent into Equation 2:

(B * $200) + (M * $225) + (P * $175) + (N * $150) = $3400
(200B) + (225M) + (175P) + (150N) = 3400

Substituting Equation 3 and 4:
(200B) + (225M) + (175(2N)) + (150N) = 3400
200B + 225M + 350N + 150N = 3400 (Expanding)

Simplifying the equation:
200B + 225M + 500N = 3400 (Combining like terms)

Now we have a system of two equations with two variables:
2B + 6N = 18
200B + 225M + 500N = 3400

By solving these equations simultaneously, we can find the values of B, M, P, and N.