A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 3 twin beds and 3 queen beds and used a total of 45 pillows. At another house, she used 53 pillows to spruce up 3 twin beds and 4 queen beds. How many decorative pillows did the realtor arrange on each bed?
Let x be the number of pillows on each twin bed.
Let y be the number of pillows on each queen bed.
From the first part of the problem, we know that 3x + 3y = 45.
From the second part of the problem, we know that 3x + 4y = 53.
Solving the system of equations, we can multiply the first equation by 4 and the second equation by 3 to eliminate x.
12x + 12y = 180
9x + 12y = 159
Subtracting the second equation from the first equation, we get 3x = 21.
Dividing both sides by 3, we get x = 7.
Substituting this value back into either equation, we get 3*7 + 3y = 45.
Simplifying the equation, we get 21 + 3y = 45.
Subtracting 21 from both sides, we get 3y = 24.
Dividing both sides by 3, we get y = 8.
Therefore, the realtor arranged 7 decorative pillows on each twin bed and 8 decorative pillows on each queen bed. Answer: \boxed{7, 8}.