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Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?

There are 16 cups in a gallon.

A. [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]

B. [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]

C. [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]

D. [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]


Sagot :

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.