There were 369 tickets purchased for a major league baseball game. the lower reserved tickets cost $9.50 and the upper box tickets costs $10.00. The total amount of money spent was $3645. How many each kind of ticket were purchased?

r + b = 365 ... 10 r + 10 b = 3650

9.5 r + 10 b = 3645

subtracting equations
... .5 r = 5

To solve this problem, we can use a system of linear equations. Let's denote the number of lower reserved tickets as "x" and the number of upper box tickets as "y".

Based on the given information, we can set up two equations:

1) The total number of tickets purchased: x + y = 369
2) The total amount spent: (9.50 * x) + (10 * y) = 3645

Now, we can solve this system of equations. There are several methods to solve them, but for this example, we will use substitution.

Let's solve equation 1 for x:

x = 369 - y

Now, substitute this expression for x in equation 2:

(9.50 * (369 - y)) + (10 * y) = 3645

Now, simplify and solve for y:

(3515.50 - 9.50y) + 10y = 3645
3515.50 + 0.50y = 3645
0.50y = 129.50
y = 129.50 / 0.50
y = 259

Now, substitute this value of y back into equation 1 to find x:

x + 259 = 369
x = 369 - 259
x = 110

So, there were 110 lower reserved tickets and 259 upper box tickets purchased.