Abigail, beth, celia, dayna, and eudora bring their dogs to the little red schoolhouse for dogs. during the morning break, they find that each of their pets has the same name as the husband for one of the other women. in particular, they notice these facts: • abigail' s dog is named george.• celia's dog is named jerry.• eudora's dog is named ike.• dayna's dog is named frank.• abigail's husband is also named frank.• beth's husband has the same name as george's wife's dog.• horace and his wife, celia, have the best-behaved dog. your job is to figure out the names of each woman's husband and eachwoman's dog. in addition, you must explain clearly how you found your answer. if you think there is more than one possibility, give all solutions, and explain why there are no more. if you think there is only one solution, explain why there are no others.

The solution has been given in the attached image

For the explanation of the question, instead of writing full names I have used the first letter of the name to indicate the wife/dog/husband. Basis the directly given information in the above paragraph, I have represented it in the format: "Wife-Dog-Husband", with '?' indicating the missing information:

Wife-Dog-Husband:

Now, we know names of all dogs except B's dog. Also, we know that each of the dog has the same name as the husband for one of the other women.

We know that C's husband is H, and a dog named H has not been tagged to any of the wives, hence H should be B's dog.

Solution so far:

Now, for the husbands we also know that Beth's husband has the same name as George's wife's dog. From this statement we definitely know that Beth's husband is not George. Also, since A's husband is F and C's is H, B's husband can be J or I.

Solution so far:

Now, D's husband can be G or I or J. And, E's husband can be G or J.

Now, going back to the information point: Beth's husband has the same name as George's wife's dog. We can see from the above that the possible wives of G are D or E. D's dog is named F, which is the name of A's husband, hence D can't be G's wife. E's dog is named I, that name has not yet been definitely tagged to any of the wives' husband. Hence, G can definitely be E's wife. This makes B's husband I (G's wife's dog). Now since I is B's husband and G is E's husband, J should be D's husband.

Hence, the final solution is:

Hence, we can see based on the information there was no possibility of multiple solutions.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6