Answer:
Sheldon should buy 5 packages to Bridget's Bakery and 3 to Penny's Pastries.
Step-by-step 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.