Let's determine which of the given expressions will correctly find the number of cups of water Katrina drinks in a week.
1 gallon is equal to 16 cups. Katrina drinks 0.5 gallons of water each day. To find the number of cups, we need to convert gallons to cups and then multiply by the number of days in a week.
Steps to solve the problem:
1. Convert the number of gallons per day to cups:
[tex]\[
0.5 \text{ gallons/day} \times \frac{16 \text{ cups}}{1 \text{ gallon}}
= 0.5 \times 16
= 8 \text{ cups/day}
\][/tex]
2. Now, we need to find out how many cups she drinks in a week:
[tex]\[
8 \text{ cups/day} \times 7 \text{ days/week}
= 8 \times 7
= 56 \text{ cups/week}
\][/tex]
Now, let's match this to the possible expressions provided:
- The first option:
[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 does not yield the correct number of cups per week because \(\frac{1 \text{ week}}{7 \text{ days}}\) dilutes the conversion instead of multiplying the days.
- The second option:
[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 also does not work because it wrongly inverts the conversion factor \(\frac{1 \text{ gallon}}{16 \text{ cups}}\) and hence, cannot correctly convert gallons to cups.
- The third option:
[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 is incorrect because it contains the wrong conversion from gallons to cups and incorrectly relates weeks and days.
- The fourth option:
[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. First, it properly converts 0.5 gallons to cups, then it multiplies by the number of days in a week to give the total number of cups per week.
Hence, 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]
