To solve the problem of how much water Katrina drinks in a week in terms of cups, we need to consider the conversion factors given and the daily consumption rate.
We start with Katrina's daily consumption which is 0.5 gallons per day. We know that there are 16 cups in 1 gallon. We also know that there are 7 days in a week.
To find the total amount of water Katrina drinks in one week, we need to use the appropriate conversion factors to change gallons to cups and days to weeks.
First, let's break down the solution step-by-step:
1. Daily water consumption: Katrina drinks 0.5 gallons each day.
2. Convert each gallon to cups: Since there are 16 cups in a gallon, we convert gallons to cups.
3. Calculate weekly consumption: Since there are 7 days in a week, we need to multiply the daily cups by 7.
We combine these steps into a single expression:
[tex]\[
\frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{16 \text{ cups}}{1 \text{ gallon}} \times \frac{7 \text{ days}}{1 \text{ week}}
\][/tex]
Each of the conversion factors ensures the units cancel appropriately:
- "gallons" cancel out,
- "days" cancel out,
- Leaving us with the total amount in "cups per week."
So, the correct expression that shows how much water Katrina drinks in a week is:
[tex]\[
\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{7 \text { days }}{1 \text { week }}
\][/tex]
Thus, the correct choice is:
[tex]\[
\frac{0.5 \text { gallons }}{1 \text { day }} \times \frac{16 \text { cups }}{1 \text { gallon }} \times \frac{7 \text { days }}{1 \text { week }}
\][/tex]
