Liann works in the olde tyme Soda shoppe. The shop sells milkshakes, double milkshakes, and triple milkshakes. A shake uses 1/8 cup of syrup, a double shake uses 1/4 cup of syrup, and a triple shake uses 3/8 cup of syrup. How many shakes of each kind could she make with 3 cups of syrup?

Syrup required for one cup of each kind

= 1/8+1/4+3/8
= 3/4 cup
1 of each : 3/4 cup
x of each : 3 cups
Cross multiply:
x = 1*3/(3/4)
=4
Lyann can make 4 of each kind of shakes.

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To determine how many shakes of each kind Liann can make with 3 cups of syrup, we need to calculate the number of each type of shake individually.

Let's start by calculating the number of regular shakes:

Since each regular shake uses 1/8 cup of syrup, we divide the total syrup (3 cups) by the syrup used for each shake:

3 cups syrup ÷ (1/8 cup syrup per shake) = 3 cups syrup × (8 shakes/1 cup syrup) = 24 shakes

Next, let's calculate the number of double shakes:

Since each double shake uses 1/4 cup of syrup, we divide the total syrup (3 cups) by the syrup used for each double shake:

3 cups syrup ÷ (1/4 cup syrup per double shake) = 3 cups syrup × (4 double shakes/1 cup syrup) = 12 double shakes

Finally, we can calculate the number of triple shakes:

Since each triple shake uses 3/8 cup of syrup, we divide the total syrup (3 cups) by the syrup used for each triple shake:

3 cups syrup ÷ (3/8 cup syrup per triple shake) = 3 cups syrup × (8/3 triple shakes/1 cup syrup) = 8 triple shakes

Therefore, with 3 cups of syrup, Liann can make 24 regular shakes, 12 double shakes, and 8 triple shakes.