6. Eliminate the Possibilities Barky, Spot, and Tiger are dogs. One is a black labrador retriever, one is a multi-colored collie, and one is a spotted dalmatian. One is owned by a doctor, one is owned by a lawyer, and one is owned by an insurance salesperson. The lawyer's dog does not have spots. The doctor's dog has more than one color. The insurance salesperson's dog is solid in color. Who owns which dog? © Glencoe/McGraw-Hill Geometry

To solve the problem, we need to analyze the clues given and eliminate possibilities step by step. ### Known Conditions: 1. **Dogs**: - Black Labrador Retriever (B) - Multi-colored Collie (C) - Spotted Dalmatian (D) 2. **Owners**: - Doctor (D) - Lawyer (L) - Insurance Salesperson (I) ### Clues: 1. The lawyer's dog does not have spots. 2. The doctor's dog has more than one color. 3. The insurance salesperson's dog is solid in color. ### Step-by-Step Analysis: 1. **From Clue 1**: The lawyer's dog does not have spots. - This means the lawyer cannot own the Spotted Dalmatian (D). 2. **From Clue 2**: The doctor's dog has more than one color. - The only dog that has more than one color is the Multi-colored Collie (C). - Therefore, the doctor must own the Multi-colored Collie (C). 3. **From Clue 3**: The insurance salesperson's dog is solid in color. - The only solid-colored dog left is the Black Labrador Retriever (B). - Therefore, the insurance salesperson must own the Black Labrador Retriever (B). 4. **Conclusion**: - Since the lawyer cannot own the Spotted Dalmatian (D) and the doctor owns the Multi-colored Collie (C), the lawyer must own the Spotted Dalmatian (D). ### Final Assignments: - **Doctor**: Multi-colored Collie (C) - **Lawyer**: Spotted Dalmatian (D) - **Insurance Salesperson**: Black Labrador Retriever (B) Thus, the ownership is as follows: - Doctor owns the Multi-colored Collie. - Lawyer owns the Spotted Dalmatian. - Insurance Salesperson owns the Black Labrador Retriever.