To determine how many cupcakes Alice can produce in 8 hours, we start by calculating her rate of production.

• Alice produces 3 dozen cupcakes in 90 minutes. Since 1 dozen equals 12 cupcakes, she produces: $3 \times 12 = 36 \text{ cupcakes in 90 minutes.}$

• Next, we calculate how many cupcakes Alice can make per minute: $\frac{36 \text{ cupcakes}}{90 \text{ minutes}} = 0.4 \text{ cupcakes per minute.}$

• Now, let's calculate how many minutes are in 8 hours: $8 \text{ hours} \times 60 \text{ minutes/hour} = 480 \text{ minutes.}$

• Finally, we calculate how many cupcakes Alice can produce in 480 minutes: $0.4 \text{ cupcakes/minute} \times 480 \text{ minutes} = 192 \text{ cupcakes.}$

So, Alice can produce 192 cupcakes in 8 hours.

Would you like any additional details or explanations?

Here are some related questions to deepen your understanding:

1. How many cupcakes can Alice produce in 5 hours?
2. If Alice’s rate of production increases by 20%, how many cupcakes would she produce in 8 hours?
3. How long would it take Alice to produce 100 cupcakes?
4. If Alice worked for 6 hours instead of 8, how many cupcakes would she make?
5. How many cupcakes could two people working at the same rate produce in 8 hours?

Tip: When dealing with rates of production, always find a unit rate (per minute, per hour, etc.) to make scaling calculations easier.