Answer :
- Calculate the minimum and maximum water Ringo needs per day: $29.75$ and $59.5$ ounces.
- Calculate the minimum and maximum water Elvis needs per day: $46.75$ and $93.5$ ounces.
- Calculate the total minimum and maximum water both dogs need per day: $76.5$ and $153$ ounces.
- Calculate the total minimum and maximum water both dogs need in a week: $535.5$ and $1071$ ounces, so the answer is $\boxed{536 Imes w Imes 1,071}$.
### Explanation
1. Problem Setup
We are given that dogs need 8.5 to 17 ounces of water each day for every 10 pounds of their weight. Ringo weighs 35 pounds and Elvis weighs 55 pounds. We need to find the range of the total amount of water they need in a week.
2. Ringo's Water Needs
First, let's calculate the minimum and maximum amount of water Ringo needs per day. Since Ringo weighs 35 pounds, he needs 35/10 times the water needed per 10 pounds. So, the minimum amount of water Ringo needs per day is $(35/10) Imes 8.5 = 3.5 Imes 8.5 = 29.75$ ounces. The maximum amount of water Ringo needs per day is $(35/10) Imes 17 = 3.5 Imes 17 = 59.5$ ounces.
3. Elvis's Water Needs
Next, let's calculate the minimum and maximum amount of water Elvis needs per day. Since Elvis weighs 55 pounds, he needs 55/10 times the water needed per 10 pounds. So, the minimum amount of water Elvis needs per day is $(55/10) Imes 8.5 = 5.5 Imes 8.5 = 46.75$ ounces. The maximum amount of water Elvis needs per day is $(55/10) Imes 17 = 5.5 Imes 17 = 93.5$ ounces.
4. Total Daily Water Needs
Now, let's calculate the total minimum and maximum amount of water both dogs need per day. The total minimum is $29.75 + 46.75 = 76.5$ ounces. The total maximum is $59.5 + 93.5 = 153$ ounces.
5. Total Weekly Water Needs
Finally, let's calculate the total minimum and maximum amount of water both dogs need in a week. The total minimum is $76.5 Imes 7 = 535.5$ ounces. The total maximum is $153 Imes 7 = 1071$ ounces. Therefore, the range of water needed in a week is approximately $535.5 Imes w Imes 1071$.
6. Final Answer
The range representing the approximate total number of ounces of water, $w$, that Elvis and Ringo need in a week is $535.5 Imes w Imes 1071$. Looking at the answer choices, the closest range is $536 Imes w Imes 1,071$.
7. Conclusion
The total amount of water that Elvis and Ringo need in a week is between 535.5 and 1071 ounces. Therefore, the correct answer is C) $536 Imes w Imes 1,071$.
### Examples
Understanding the water needs of pets based on their weight is crucial for their health. This calculation can be applied to various scenarios, such as planning for pet care during travel or ensuring adequate hydration during different seasons. For instance, a dog walker can use this information to carry the right amount of water for multiple dogs, or a pet owner can adjust water intake based on weather conditions to prevent dehydration.
- Calculate the minimum and maximum water Elvis needs per day: $46.75$ and $93.5$ ounces.
- Calculate the total minimum and maximum water both dogs need per day: $76.5$ and $153$ ounces.
- Calculate the total minimum and maximum water both dogs need in a week: $535.5$ and $1071$ ounces, so the answer is $\boxed{536 Imes w Imes 1,071}$.
### Explanation
1. Problem Setup
We are given that dogs need 8.5 to 17 ounces of water each day for every 10 pounds of their weight. Ringo weighs 35 pounds and Elvis weighs 55 pounds. We need to find the range of the total amount of water they need in a week.
2. Ringo's Water Needs
First, let's calculate the minimum and maximum amount of water Ringo needs per day. Since Ringo weighs 35 pounds, he needs 35/10 times the water needed per 10 pounds. So, the minimum amount of water Ringo needs per day is $(35/10) Imes 8.5 = 3.5 Imes 8.5 = 29.75$ ounces. The maximum amount of water Ringo needs per day is $(35/10) Imes 17 = 3.5 Imes 17 = 59.5$ ounces.
3. Elvis's Water Needs
Next, let's calculate the minimum and maximum amount of water Elvis needs per day. Since Elvis weighs 55 pounds, he needs 55/10 times the water needed per 10 pounds. So, the minimum amount of water Elvis needs per day is $(55/10) Imes 8.5 = 5.5 Imes 8.5 = 46.75$ ounces. The maximum amount of water Elvis needs per day is $(55/10) Imes 17 = 5.5 Imes 17 = 93.5$ ounces.
4. Total Daily Water Needs
Now, let's calculate the total minimum and maximum amount of water both dogs need per day. The total minimum is $29.75 + 46.75 = 76.5$ ounces. The total maximum is $59.5 + 93.5 = 153$ ounces.
5. Total Weekly Water Needs
Finally, let's calculate the total minimum and maximum amount of water both dogs need in a week. The total minimum is $76.5 Imes 7 = 535.5$ ounces. The total maximum is $153 Imes 7 = 1071$ ounces. Therefore, the range of water needed in a week is approximately $535.5 Imes w Imes 1071$.
6. Final Answer
The range representing the approximate total number of ounces of water, $w$, that Elvis and Ringo need in a week is $535.5 Imes w Imes 1071$. Looking at the answer choices, the closest range is $536 Imes w Imes 1,071$.
7. Conclusion
The total amount of water that Elvis and Ringo need in a week is between 535.5 and 1071 ounces. Therefore, the correct answer is C) $536 Imes w Imes 1,071$.
### Examples
Understanding the water needs of pets based on their weight is crucial for their health. This calculation can be applied to various scenarios, such as planning for pet care during travel or ensuring adequate hydration during different seasons. For instance, a dog walker can use this information to carry the right amount of water for multiple dogs, or a pet owner can adjust water intake based on weather conditions to prevent dehydration.
