Tia is buying paper cups and plates. Cups come in packages of 12, and plates come in packages of 10. She wants to buy the same number of cups and plates, but plans to buy the least number of packages possible. How much should Tia expect to pay if each package of cups is $3 and each package of plates is $5? Explain. Thanks
The least common multiple of 10 and 12 is 60.
60/10 = 6 packages of plates
60/12 = 5 packages of cups
45
Here would have to buy six packages of plates in five packages of cups because 10 and 12 calcium is 60
I dont know how to do math it's so hard
i did 10x6=60 and 12x5=60 3x5=15 5x6=30 30+15=45
i think this is right but not to sure
To solve this problem, we need to find the least common multiple (LCM) of 12 and 10. The LCM represents the least number that both 12 and 10 can evenly divide into. In this case, it will tell us how many cups and plates Tia needs to buy to have the same number.
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 ÷ 12 cups/package = 5 packages of cups.
Similarly, plates come in packages of 10, so Tia would need 60 plates ÷ 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 × $3/package = $15.
The cost of each package of plates is $5, so the total cost of the plates would be 6 packages × $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.