The owner of Castroville Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 9 small arrangements and 9 large arrangements, which took her a total of 90 minutes. After lunch, she arranged 5 small arrangements and 6 large arrangements, which took 56 minutes. How long does it take to assemble each type?
Let s be the number of minutes per small arrangement and l be the number of minutes per large arrangement.
We know that s*9 + l*9 = 90 and s*5 + l*6 = 56.
Multiplying the first equation by 5 and the second equation by 9, we get 5s*9 + 5l*9 = 450 and 9s*5 + 9l*6 = 504.
Multiplying the third equation by -9/5, we get -9s - 9l*6 = -504.
Adding the second and third equation, we get 9s*5 - 9s - 9l*6 - 9l*6 = 504 - 504.
Combining like terms, we get -45l = 0.
Dividing both sides by -45, we get l = 0.
Substituting this value back into the second equation, we get s*5 + 0*6 = 56
Therefore, s*5 = 56.
Dividing both sides by 5, we get s = 56/5 = <<56/5=11.2>>11.2
Therefore, it takes 11.2 minutes to assemble each small arrangement. Answer: \boxed{11.2}.