Let's break this problem down step by step!
1. **Understanding the problem**: We have two barrels with the same amount of honey in them. Then, honey is taken out from both barrels. After drawing the honey, the amount of honey left in one barrel is seven times more than the amount left in the other barrel.
2. **Let’s use a variable**: Let's say each barrel originally had H gallons of honey.
3. **Draw the honey**: From the first barrel, we draw 37 gallons, so the honey left in that barrel is:
First Barrel: H - 37
From the second barrel, we draw 7 gallons, so the honey left in that barrel is:
Second Barrel: H - 7
4. **Setting up an equation**: According to the problem, the honey left in the first barrel is seven times the honey left in the second barrel. We write this as an equation:
H - 37 = 7 * (H - 7)
5. **Solving the equation**: Let's solve the equation step by step.
First, we expand the equation:
H - 37 = 7H - 49
Now, we want to get all the H terms on one side. We do this by subtracting H from both sides:
-37 = 6H - 49
Next, we add 49 to both sides:
12 = 6H
Now, divide both sides by 6:
H = 2
6. **Finding the original amount**: Since H = 2 gallons, each barrel originally contained 2 gallons of honey.
So, in conclusion, each barrel initially had 2 gallons of honey.