Answer: She needs 6 packs of cookies and 5 packs of coffee sachets.
Explanation:
Cookies: come in packs of 10
Coffee sachets: come in packs of 12.
Sally wants to sell them in groups of 1 cookie and 1 coffee sachet, then we need to find a common multiple of 10 and 12. (the smallest one in this case).
To find the smallest common multiple, first let's find the largest common factor between 10 and 12.
If we write the numbers as a product of prime numbers, we have:
10 = 2*5
12 = 2*3*3
The only common factor is 2.
Then the smallest common multiple between 10 and 12 is equal to the product of 10 and 12 divided by the largest common factor between them, in this case is 2.
M = 10*12/6 = 60
Now to find the number of packages of each thing that she must buy, we need to divide 60 by the number of elements in each pack.
Cookies: 10 per pack
60/10 = 6
She needs 6 packs of cookies
Coffe: 12 per pack
60/12= 5
She needs 5 packs of coffee sachets.