Final answer:
The correct indication of fluid volume deficit in a client with vomiting and diarrhea for three days is dry mucous membranes and decreased urine output, which align with the symptoms of dehydration.
Step-by-step explanation:
A client who reports vomiting and diarrhea for the past three days could be experiencing signs of fluid volume deficit also known as dehydration. Among the options given, the finding that should most strongly indicate to a nurse that the client is experiencing fluid volume deficit is dry mucous membranes. Other signs of fluid volume deficit include decreased urine output since the body would conserve water to deal with dehydration. Increased blood pressure and weight gain are not typically associated with dehydration; blood pressure may decrease, and weight is likely to drop due to fluid loss from prolonged symptoms such as vomiting and diarrhea.