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?

Rationale

Ms. Waters made 8 family visits on Tuesday.

To solve for the number of family visits made on Tuesday, we set up equations based on the information given. Let the number of visits on Monday be x. Thus, on Tuesday, she made x + 4 visits. The total visits for the first two days is x + (x + 4) = 2x + 4. The visits for the last three days are three times this amount, which leads us to find that she made 8 visits on Tuesday.

A (3) YOUR ANSWER

If Ms. Waters made 3 visits on Tuesday, then that would imply she made -1 visit on Monday, which is impossible. The number of visits on Monday must be a non-negative integer.

B (4) YOUR ANSWER

If Ms. Waters made 4 visits on Tuesday, then on Monday she would have made 0 visits. The total visits for the last three days would then be calculated incorrectly, leading to a total that does not equal 30 reports.

C (6) YOUR ANSWER

If Ms. Waters made 6 visits on Tuesday, then on Monday she would have made 2 visits. The total visits for the first two days would be 8. This results in 24 visits for the last three days, giving a total of 32 visits, which does not match the 30 reports.

D (7) YOUR ANSWER

If Ms. Waters made 7 visits on Tuesday, then she must have made 3 visits on Monday. The total visits for the first two days would be 10. Accordingly, the last three days would yield 30 visits, leading to a total of 40 visits, which is also incorrect.

E (8) CORRECT

If Ms. Waters made 8 visits on Tuesday, she must have made 4 visits on Monday. This results in a total of 12 visits for the first two days. The last three days would then amount to 36 visits, leading to a total of 30 reports, which is consistent with the information provided.

Conclusion

Through logical deductions and calculations, we conclude that Ms. Waters made 8 family visits on Tuesday. This fits the framework of the problem, confirming that her total visits across the week align with the number of anecdotal reports written, thereby validating the solution.

Ms. Waters made 8 family visits on Tuesday.

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