10. Ms. Waters, a social worker, made family visits Monday through Friday last week and wrote ane\cdotal reports on ? of the visits. She made 4 more visits on Tuesday than on Monday and 3 × as many total visits during the last three days as during the first two days. If she wrote a total of 30 ane\cdotal reports last week, how many family visits did she make on Tuesday?
Answer: E
Ms. Waters made 8 family visits on Tuesday.
To determine the number of family visits Ms. Waters made on Tuesday, we can analyze the provided information and equations. Given that she made 4 more visits on Tuesday than on Monday and that the total visits during the last three days were three times that of the first two days, we find that she made 8 visits on Tuesday.
A) 3
If Ms. Waters made 3 visits on Tuesday, then she would have made -1 visit on Monday, which is impossible. Therefore, this option is incorrect.
B) 4
If she had made 4 visits on Tuesday, this means she made 0 visits on Monday (since she made 4 more visits on Tuesday than on Monday). This would not account for the total number of visits required based on her reports. Hence, this option is also incorrect.
C) 6
Should Ms. Waters have made 6 visits on Tuesday, she would have made 2 visits on Monday. This leads to a total of 8 visits in the first two days. For the last three days, she would need to make 24 visits (3 times the first two days), which is inconsistent with the 30 reports written. Thus, this option is incorrect.
D) 7
If Ms. Waters made 7 visits on Tuesday, she would have made 3 visits on Monday. This would lead to a total of 10 visits in the first two days. To meet the requirement of 30 reports, she would need to make 20 visits in the last three days, which is not feasible given the constraints. Therefore, this option is incorrect.
E) 8
If she made 8 visits on Tuesday, this means she made 4 visits on Monday. This results in 12 visits across the first two days. For the last three days, she would need to make 36 visits (3 times the first two days), which aligns with the reports written. This option is correct.
Conclusion
Ms. Waters made a total of 8 visits on Tuesday, which is the only option that fits all given conditions regarding her visits and the number of reports she wrote. All other options fail to meet the logical requirements of the problem based on the relationships provided for her family visits.