Helen gathered 37 mushrooms in three hours. how many mushrooms did she gather every hour, if she gathered 7 more mushrooms in the second hour than in the first hour, and 6 more in the third hour than in the first hour?

Let x be the amount of gathered mushrooms during first hour, then x
+7 is the amount of gathered mashrooms during the second hour and x+6 -- during the third hour. In total it will be x+(x+7)+(x+6) that is equal to 37.
3x+13=37, then 3x=24 and x=24÷3=8
During the first hour she gathered 8 mushrooms, 8+7=15 mushrooms she gathered during second hour and 8+6=14 she gathered during the third hour.