Two barrels contain equal quantities of honey from one barrel 37 gallons of honey or drone from the other barrel 7 gallons of honey are drawn the quantity remaining in winnsboro is now seven times that remaining in the other barrel how much did each barrel contain at first

At the start, each barrel has the same amount of honey, so:

Barrel 1 has X gallons

Barrel 2 has X gallons.

from 1, they extract 37 gallos, and from 2 they extract 7 gallons, so now:

Barrel 1 has X - 37

Barrel 2 has X- 7

and now, the quantity in the Barrel 2 is seven times the quantity in the barrel 1, so:

X- 7 = 7*(X - 37)

we need to find X.

X - 7 = 7*X - 37*7 = 7*X - 259

X - 7*X = 7 - 259

-6*X = -252

X = 252/6 = 42

So at the start, each barrel has 42 gallons of honey.