Bridget's Bakery sells cupcakes in packeges of 6. Penny's Pastries sells cupcakes in packages of 10. Sheldon wants to buy the same number of cupcakes from each bakery for a party, and he can buy only buy cupcakes in packages.

Sheldon should buy 5 packages to Bridget's Bakery and 3 to Penny's Pastries.

Explanation:

In order to buy the same amount of cupcakes from both stores, Sheldon should buy 5 packages to Bridget's Bakery and 3 to Penny's Pastries. To calculate this, Sheldon should calculate the least common multiple between 6 and 10, which is the number of cupcakes that each package has. The lest common multiple is the smallest positive integer that is divisible by both numbers (in this case, 6 and 10). To find the least common multiple Sheldon should calculate the prime factorization of 6 and 10, that is to say, which prime numbers multiply together to make the original number.

6 = 2x3

10=2x5

After that, Sheldon should multiply each factor the greatest number of times it occurs, in this case:

2x3x5 = 30

That means he needs to buy 30 cupcakes from each store. 30 divided by 6 is 5, and 30 divided by ten is 3. Those are the numbers of packages he needs.

Sheldon has to buy 10 packages from Bridget's Bakery, and 6 packages from Penny's Pastries.