To find the least number of packs of regular dog food Jerry needs to get in order to have the same weight of each type of dog food, we can set up the problem using the weights of the dog food packs.
Let \( x \) be the number of packs of regular dog food (8 pounds each) and \( y \) be the number of packs of diet dog food (10 pounds each). We need to find the smallest \( x \) such that the total weight of regular dog food equals the total weight of diet dog food:
\[ 8x = 10y \]
This can be rearranged to find the relationship between \( x \) and \( y \):
\[ \frac{x}{y} = \frac{10}{8} = \frac{5}{4} \]
This implies that for every 5 packs of regular dog food, Jerry needs 4 packs of diet dog food.
To find the least number of packs, we can set \( y = 4 \) (the quantity needed for the diet dog food) and calculate \( x \):
\[ x = \frac{5}{4}y = \frac{5}{4} \cdot 4 = 5 \]
Therefore, Jerry needs at least 5 packs of regular dog food.
To verify:
- Total weight of regular dog food: \( 5 \times 8 = 40 \) pounds
- Total weight of diet dog food (using \( y = 4 \)): \( 4 \times 10 = 40 \) pounds
Both totals are indeed equal, confirming our solution.
The least number of packs of regular dog food Jerry needs is \( \boxed{5} \).