A museum had 25% more visitors on Sunday than on Saturday, and on Monday it had 40% fewer visitors than on Sunday. If Monday's count fell 105 short of Saturday's, how many visitors came on Saturday?

Let Saturday be $S$. Then Sunday = 1.25$S$ and Monday = $0.60\times 1.25S=0.75S$. The gap is $S-0.75S=0.25S=105$, so $S=420$. Check: Saturday 420, Sunday 525, Monday 315, and 420 - 315 = 105. 700 comes from treating the net as 25 - 40 = -15%, which would make Monday 0.85$S$ and the gap 0.15$S$; the 40% cut acts on Sunday's 525, not on Saturday's figure. 525 and 315 are Sunday's and Monday's counts.