Answer:
12 inches × 12 inches × 12 inches
Step-by-step explanation:
Cube volume is 

![s=\sqrt[3]{1728}](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B3%5D%7B1728%7D)

Step-by-step explanation:
In Kate's equation, 20 is the total number of tickets, 4 is number of tickets per ride, r is number of rides already ridden, and 4r is the number of tickets used
in Brian's equation, 5 is total number of rides Katie can ride and 5 - r is the number of rides left to ride
76+20x
factor out 4
4 (19+5x)
so one possible dimensions of the rectangle is 4 by 19+5x
He wanted the mathematical challenge