Problem Solving

I have solved this problem, but wrong. Could someone please tell me where I have gone wrong in my solution? Thanks so much!

The table above gives the type and number of pets owned by a group of 48 households that own only cats and dogs. If the ratio of the total number of cats to the total number of dogs is 5:3, how many dogs are there?

Type of Pet Number of Households Avg. # of Pets/Household

Dogs Only 16 1.5

Cats Only 24 1.25

Dogs & Cats 8 3.25

Answer choices:

18, 24, 30, 36, 48


My (incorrect) solution:

Total # of Dogs @ Dog Only Households: 16 * 1.5 = 24
Total # of Cats @ Cat Only Households: 24 * 1.25 = 30
Total # of pets @ Dog & Cat Households: 8 * 3.25 = 26

For pets in the Dog & Cat Households only, I will label dogs D and cats C

Therefore:

D + C = 24... rearranged: C = 24 - D

Keeping with the ratio:

5 / 3 = (30 + C) / (24 + D)

5(24 + D) = 3(30 + C)

120 + 5D = 90 + 3C

Substitute in for C:

120 + 5D = 90 + 3(24 - D)

120 + 5D = 90 + 72 - 3D

120 + 5D = 162 - 3D

8D = 42

D = 42 / 8 = 5 1/4

5 1/4 + 24 = 29 1/4

Where have I gone wrong? I have looked over this solution several times and cannot for the life of me figure out where I have gone wrong?

I know there is an easier way to do this (24 + 30 + 26 = 80... given the ratio 5:3, there are 3 dogs for every 8 animals, so therefore there are 30 dogs). I am just wondering where my logic & solution goes wrong.

Thanks so much for your help!