To find the number of cups of water Katrina drinks in a week, let's break down the problem step by step.
1. Determine how many cups of water Katrina drinks per day:
- Katrina drinks 0.5 gallons of water per day.
- Since there are 16 cups in 1 gallon, we multiply 0.5 gallons by 16 cups per gallon to find the number of cups she drinks per day.
[tex]\[
0.5 \text{ gallons} \times 16 \text{ cups/gallon} = 8 \text{ cups/day}
\][/tex]
2. Determine how many cups of water Katrina drinks in a week:
- There are 7 days in a week.
- We multiply the number of cups she drinks per day by the number of days in a week to find the total number of cups she drinks in a week.
[tex]\[
8 \text{ cups/day} \times 7 \text{ days/week} = 56 \text{ cups/week}
\][/tex]
Thus, Katrina drinks 56 cups of water in a week.
Now, let's analyze the expressions given in the question:
1. [tex]\(\frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{16 \text{ cups}}{1 \text{ gallon}} \times \frac{1 \text{ week}}{7 \text{ days}}\)[/tex]
- This expression converts gallons to cups correctly but uses incorrect conversion for days to weeks.
2. [tex]\(\frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{1 \text{ gallon}}{16 \text{ cups}} \times \frac{7 \text{ days}}{1 \text{ week}}\)[/tex]
- This expression incorrectly reverses the cup-to-gallon conversion factor.
3. [tex]\(\frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{1 \text{ gallon}}{16 \text{ cups}} \times \frac{1 \text{ week}}{7 \text{ days}}\)[/tex]
- This expression incorrectly reverses the cup-to-gallon conversion factor and uses incorrect conversion for days to weeks.
4. [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 is the correct expression as it uses the correct conversions:
- It properly converts gallons to cups.
- It correctly converts days to weeks.
Therefore, the expression that shows how to find the number of cups of 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]
This expression simplifies to:
[tex]\[
0.5 \times 16 \times 7 = 56
\][/tex]
So, Katrina drinks 56 cups of water in a week.
