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 5 twin beds and 4 queen beds and used a total of 76 pillows. At another house, she used 36 pillows to spruce up 2 twin beds and 2 queen beds. How many decorative pillows did the realtor arrange on each bed? The realtor used pillows on every twin bed and pillows on every queen bed.
Let x be the number of pillows on each twin bed and y be the number of pillows on each queen bed.
From the first house:
5x + 4y = 76
From the second house:
2x + 2y = 36
Solve the above system of equations to find x and y:
From the second equation, x + y = 18
2x + 2y = 36
Divide by 2:
x + y = 18
x = 18 - y
Substitute x into the first equation:
5(18 - y) + 4y = 76
90 - 5y + 4y = 76
-y = -14
y = 14
Substitute y back into x = 18 - y:
x = 18 - 14
x = 4
Therefore, the realtor arranged 4 decorative pillows on each twin bed and 14 decorative pillows on each queen bed.