The least common multiple of 10 and 12 is 60.
60/10 = 6 packages of plates
60/12 = 5 packages of cups
60/10 = 6 packages of plates
60/12 = 5 packages of cups
i think this is right but not to sure
To find the LCM, we can start by listing the multiples of each number until we find a common multiple:
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The first common multiple we find is 60. Therefore, Tia needs to buy 60 cups and 60 plates.
Since cups come in packages of 12, Tia would need 60 cups รท 12 cups/package = 5 packages of cups.
Similarly, plates come in packages of 10, so Tia would need 60 plates รท 10 plates/package = 6 packages of plates.
The cost of each package of cups is $3, so the total cost of the cups would be 5 packages ร $3/package = $15.
The cost of each package of plates is $5, so the total cost of the plates would be 6 packages ร $5/package = $30.
Therefore, Tia should expect to pay $15 + $30 = $45 if each package of cups costs $3 and each package of plates costs $5.