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 she wants to buy the least number of packages possible. How much should Tia expect to pay if each package of cups costs $3 and each package of plates costs $5? Explain.

1) We need to find, what is the smallest number, when the number of plates and cups are going to be the same. Cups come in packages of 12, and plates come in packages of 10. That means that we need to find least common multiple for 12 and 10.

12=2*2*3

10=2*5

Least common multiple = 2*2*3*5 = 60

Number of cups should be = 60, and number of plates should be = 60 also.

2) 60 : 12 = 5 packages of cups

60 : 10 = 6 packages of plates.

3) 5*3=15 ($) Tia expect to pay for cups.

6*5=30 ($) Tia expect to pay for plates.

4) 15 + 30 = $ 45 Tia expect to pay for cups and plates.