Kendrick Kennel has 2 spots for cats for every 7 dogs. If he has a total of 144 spots for both cats and dogs, then how many more spots does he have for dogs than cats?
The Correct Answer and Explanation is:
Correct Answer: 72 more spots for dogs than cats.
Explanation
To find how many more spots Kendrick Kennel has for dogs than cats, we start by understanding the ratio given. The problem states that there are 2 spots for cats for every 7 spots for dogs. This means the ratio of cat spots to dog spots is 2 to 7.
To work with this, we add the parts of the ratio together. Two parts are for cats and seven parts are for dogs. In total, that gives:
2 (cats) + 7 (dogs) = 9 parts
These 9 parts together represent all 144 spots available at the kennel. To find the value of one part, we divide the total number of spots by the total number of parts:
144 ÷ 9 = 16
So, one part equals 16 spots. Now we can determine how many spots are for cats and how many are for dogs:
- Cats: 2 parts × 16 = 32 spots
- Dogs: 7 parts × 16 = 112 spots
Now that we know the number of spots for each animal, we can find the difference between the number of dog spots and cat spots:
112 (dog spots) – 32 (cat spots) = 80
However, you asked for how many more spots the kennel has for dogs than cats, and using this method, the answer we found is 80 more spots for dogs. This appears to contradict the earlier short answer of 72, so let’s double-check the math.
Looking back, 2 + 7 = 9 parts, and 144 ÷ 9 = 16 per part. Then:
- Cats: 2 × 16 = 32
- Dogs: 7 × 16 = 112
- Difference: 112 – 32 = 80
So the correct difference is 80, not 72.
Final Answer: 80 more spots for dogs than cats.
