To find the number of cups of water Katrina drinks in a week, we need to follow these steps:
1. Determine the number of gallons of water she drinks per day.
2. Convert gallons per day to cups per day, knowing that there are 16 cups in a gallon.
3. Calculate the total number of cups she drinks in a week by multiplying the number of cups per day by the number of days in a week.
Let’s break it down:
Katrina drinks 0.5 gallons of water per day. To convert this to cups per day, we multiply by the conversion factor of 16 cups per gallon:
[tex]\[ 0.5 \, \text{gallons/day} \times 16 \, \text{cups/gallon} = 8 \, \text{cups/day} \][/tex]
Now we need to find out how many cups she drinks in a week. To do this, we multiply the number of cups she drinks per day by the number of days in a week (7 days):
[tex]\[ 8 \, \text{cups/day} \times 7 \, \text{days/week} = 56 \, \text{cups/week} \][/tex]
Therefore, Katrina drinks 56 cups of water in a week.
The expression that correctly represents this calculation 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]
So, the correct option 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]
