The Berlin Papyrus was partly decoded and published in 1862, a year before the British Museum received the RMP and the EMLR from the estate of Henry Rhind.
The Berlin Papyrus contains two second degree equations, each associated with x and y stated in a proportional relationship.
x^2 + y^2 = 100
x^2 + y^2 = 400
A clear understanding of the scribal solution was published in 1900 by H. Schack-Schackenberg within a pesu problem discussed in RMP 69 and Ahmes' pesu proportional solutions solved in RMP 69-78, all scaled the number of hekats of grain needed to produce n loaves of bread.
In RMP 69 3 + 1/2 hekats of grain produced 80 loaves of bread.
The scribal solution is discussed on Planetmath per:
The standard 1920s scholars Peet, Chace, et al, followed by Gillings 1970, Robins-Shute 1987 and Clagett 1999 failed to stress Schack-Schackenberg's common proportional solution to both problems, each for a different personal reason.
After 2000 a new path to reading 2/n tables and unit fraction arithmetic arrived on the scene, fully accepting Schack-Schackenberg's solution with no reservations.