At the Sacramento Monarchs home games, Row 1 seats cost $35 each and Row 2 seats cost $30 each. The 105 seats in these rows were sold out for the season. The total receipts for them were $3420. How many of each seat were sold?

number of row1 seats --- x

number of row2 seats --- 105-x

35x + 30(105-x) = 3420

easy to solve for x
sub back into my definition.

35x+3150-30x=3420

5x=270
x=270

Row 1 54 seats
Row 2 51 seats

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the number of Row 1 seats as "x" and the number of Row 2 seats as "y".

From the given information, we know that the total number of seats sold is 105:
x + y = 105 (Equation 1)

We also know that the total receipts for all the seats sold is $3420. The price for each Row 1 seat is $35, and the price for each Row 2 seat is $30. We can use these prices and the number of seats from Equation 1 to get another equation for the total receipts:
35x + 30y = 3420 (Equation 2)

Now, we have a system of two equations with two variables (x and y). We can solve this system to find the values of x and y.

One way to solve this system is by substitution. We can solve Equation 1 for x, giving:
x = 105 - y

Substitute this value of x into Equation 2:
35(105 - y) + 30y = 3420

Now, we can simplify and solve for y:
3675 - 35y + 30y = 3420
-5y = -255
y = 51

Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x + 51 = 105
x = 105 - 51
x = 54

Therefore, 54 Row 1 seats and 51 Row 2 seats were sold.