Final answer:
Mia must buy 3 packages of noisemakers and 4 packages of party hats to have equal numbers of each, with the total cost being $66.
Step-by-step explanation:
Mia wants to buy equal numbers of noisemakers and party hats for the lowest possible cost.
Noisemakers come in packages of 12 for $2 each, and party hats come in packages of 9 for $15 each.
To find the least amount of money Mia can spend, we must find the least common multiple (LCM) of the number of items in each package so that she can have an equal number of each item.
The least common multiple of 12 and 9 is 36, which means Mia needs to buy 36 noisemakers and 36 hats. However, since they come in packages, we have to determine how many packages she needs.
For noisemakers, 36 noisemakers divided by 12 per package equals 3 packages of noisemakers.
For hats, 36 hats divided by 9 per package equals 4 packages of party hats.
To calculate the total cost, we multiply the number of packages by the cost per package.
For noisemakers, 3 packages at $2 each comes to $6.
For hats, 4 packages at $15 each comes to $60.
Therefore, the total cost for both items is $6 (noisemakers) + $60 (hats) = $66.
Complete question:
At a party store, packages of 12 noisemakers are $2 each. Packages of 9 party hats are $15 each. Mia wants to buy equal numbers of noisemakers and hats.
What is the least amount of money Mia can spend?
To get that many noisemakers and hats:
How many packages of noisemakers does Mia need to buy?
How many packages of hats?
If Mia buys that many packages of each item, what is her total cost? Show your work.