To find the number of cups of water Katrina drinks in a week, we need to convert the amount she drinks daily in gallons to weekly in cups. We'll apply dimensional analysis to convert from gallons per day to cups per week step-by-step.
First, we know these key conversion factors:
1. Katrina drinks 0.5 gallons of water per day.
2. There are 16 cups in 1 gallon.
3. There are 7 days in 1 week.
Let's analyze each of the given options to determine which one correctly uses these conversions:
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 option multiplies the amount of water Katrina drinks in gallons per day by the number of cups per gallon, and then incorrectly divides by the number of days in a week. This does not align dimensions correctly to get cups per week.
Hence, it is incorrect.
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 option incorrectly inverts the cup-to-gallon ratio and multiplies by the number of days per week. This conversion creates a wrong dimensional analysis.
Hence, it is incorrect.
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 option also incorrectly inverts the cup-to-gallon ratio and incorrectly misses multiplying by the number of days in a week.
Hence, it is incorrect.
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 option correctly multiplies the number of gallons per day by the number of cups per gallon and the number of days per week. It uses the conversion factors correctly and aligns dimensions to get the result in cups per week.
Hence, it is correct.
Therefore, 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]
So the correct option is:
[tex]\(\boxed{\frac{0.5 \text{ gallons}}{1 \text{ day}} \times \frac{16 \text{ cups}}{1 \text{ gallon}} \times \frac{7 \text{ days}}{1 \text{ week}}}\)[/tex]
