Dogs need 8.5 to 17 ounces of water each day for every 10 pounds of their weight. Everett has two dogs-Ringo is a 35-pound black lab mix,and Elvis is a 55-pound beagle. Which of the following ranges represents the approximate total number of ounces of water,w, that Elvis and Ringo need in a week?

Options

A. `77 le w le 153`
B. `109 le w le 218`
C. `536 le w le 1,071`
D. `765 le w le 1,530`

Answer

To solve the problem, we need to calculate the total amount of water that Ringo and Elvis need in a week based on their weights and the daily water requirement per 10 pounds of weight.

### Step-by-Step Solution

1. **Determine the daily water requirement for each dog:**
- The daily water requirement for dogs is between 8.5 to 17 ounces for every 10 pounds of weight.
- For Ringo (35 pounds):
- Daily requirement = (35 pounds / 10 pounds) * (8.5 to 17 ounces)
- Daily requirement = 3.5 * (8.5 to 17 ounces)
- Daily requirement = (29.75 to 59.5 ounces)
- For Elvis (55 pounds):
- Daily requirement = (55 pounds / 10 pounds) * (8.5 to 17 ounces)
- Daily requirement = 5.5 * (8.5 to 17 ounces)
- Daily requirement = (46.75 to 93.5 ounces)

2. **Calculate the total daily water requirement for both dogs:**
- Total daily requirement = Ringo's daily requirement + Elvis's daily requirement
- Total daily requirement = (29.75 to 59.5 ounces) + (46.75 to 93.5 ounces)
- Total daily requirement = (29.75 + 46.75) to (59.5 + 93.5)
- Total daily requirement = (76.5 to 153 ounces)

3. **Calculate the weekly water requirement:**
- Since there are 7 days in a week, multiply the daily requirement by 7.
- Total weekly requirement = (76.5 to 153 ounces) * 7
- Total weekly requirement = (535.5 to 1071 ounces)

4. **Final range of water requirement for a week:**
- The total amount of water needed by Ringo and Elvis in a week is between 535.5 ounces and 1071 ounces.
- Rounding to the nearest whole number gives us the range: 536 to 1071 ounces.

### Conclusion
The approximate total number of ounces of water, \( w \), that Elvis and Ringo need in a week is in the range of \( 536 < w < 1071 \).