Set up a system of equations describing the following word problem. Be sure to specify what each variable represents.
Ayako spent $7.80 on equal weights of white and red beads. The red beads cost twice as much per ounce as the white beads. Well, sure they do. The world's supply of the color red has recently dipped to an all-time low, and is in high demand.
How much did Ayako spend on each color of beads?