Tia is buying paper cups and plates cops 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 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

The easiest way to do this is to work out the lowest common multiple of 10 and 1 by listing the multiples:

12: 12,24,36,48,60,72
10: 10,20,30,40,50,60

We can then see that the lowest number of plates and cups is 60 of each.

We can then work out the costs:

Cups:
60 total = 5 packages
5 packages = $15

Plates:
60 total = 6 packages
6 packages = $30

The total cost is then $15 + $30 = $45

The linear equation is: y=ax+b