To determine how many cups of water Katrina drinks in a week, we need to perform a dimensional analysis considering the given conditions. Here are the steps to follow:
1. Daily Water Consumption in Gallons:
Katrina drinks 0.5 gallons of water per day.
2. Convert Gallons to Cups:
There are 16 cups in one gallon.
3. Calculate for the Entire Week:
There are 7 days in a week.
We need to set up an expression that allows us to multiply these values properly to get the total number of cups Katrina drinks in a week.
### Step-by-Step Breakdown:
1. Start with Katrina's daily intake in gallons:
[tex]\[
\frac{0.5 \text{ gallons}}{1 \text{ day}}
\][/tex]
2. Convert gallons to cups:
[tex]\[
\frac{16 \text{ cups}}{1 \text{ gallon}}
\][/tex]
3. Calculate for the number of days in a week:
[tex]\[
\frac{7 \text{ days}}{1 \text{ week}}
\][/tex]
The correct expression multiplies these ratios together:
[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]
This multiplication ensures that gallons, days, and weeks properly cancel out, leaving us with the number of cups per week as the final unit.
So, the correct expression 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]
Therefore, 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]
This corresponds to the last option in the given choices. Thus, the correct index of the choice is 4.
