Liann works in the old time soda shoppe the shop sells shakes. a single shake uses 1/8 cup syrup, a double shake uses 1/4 cup syrup, a tripple milk shake uses 3/8 cup syrup. How many shakes can she make of each with 3 cups of syrup?

Do you mean how many single shakes could she make with 3 cups of syrup, then how many double shakes could she make, and how many triples? Or, do you need to mix and match the shake sizes?

mix and match the shake sizes to equal using 3 cups

The question asks how many shakes of each size can be made.

Single:
(1/8) / 3 = 8 * 3 = 24 shakes

Double:

Triple:

24 shakes

To find out how many shakes Liann can make of each type with 3 cups of syrup, we need to divide the total amount of syrup by the amount of syrup used for each type of shake.

Let's start with the single shake:
The single shake uses 1/8 cup of syrup.
So, to find the number of single shakes Liann can make, we divide 3 cups by 1/8 cup:

(3 cups) / (1/8 cup) = 3 * (8/1) = 3 * 8 = 24

Therefore, with 3 cups of syrup, Liann can make 24 single shakes.

Now let's move to the double shake:
The double shake uses 1/4 cup of syrup.
So, to find the number of double shakes Liann can make, we divide 3 cups by 1/4 cup:

(3 cups) / (1/4 cup) = 3 * (4/1) = 3 * 4 = 12

Therefore, with 3 cups of syrup, Liann can make 12 double shakes.

Lastly, let's calculate the number of triple shakes:
The triple shake uses 3/8 cup of syrup.
So, to find the number of triple shakes Liann can make, we divide 3 cups by 3/8 cup:

(3 cups) / (3/8 cup) = 3 * (8/3) = 3 * 2.67 ≈ 8

Therefore, with 3 cups of syrup, Liann can make approximately 8 triple shakes.

In summary:
- Liann can make 24 single shakes with 3 cups of syrup.
- Liann can make 12 double shakes with 3 cups of syrup.
- Liann can make approximately 8 triple shakes with 3 cups of syrup.