Final answer:
The city spent parts of its budget on several categories. After calculating the fractions of the budget spent on buildings and maintenance, administrative personnel, and public safety, we find that B/8 of the budget is left for other expenses.
Step-by-step explanation:
The city spent 1/4 of its budget on buildings and maintenance, which is 1/8 less than what it spent on administrative personnel. So if B represents the total budget, the amount spent on administrative personnel is B/4 + B/8. The amount spent on public safety can then be calculated as B/4 + B/8 - B/8. After simplifying, that leaves us with B/4 for public safety. To find the amount left for other expenses, we subtract the portions for buildings and maintenance (B/4), administrative personnel (B/4 + B/8), and public safety (B/4) from the total budget (B).
Calculating the fractions, we get:
- Buildings and maintenance: B/4
- Administrative personnel: B/4 + B/8 = (2B/8) + (B/8) = 3B/8
- Public safety: B/4 (since administrative personnel is B/8 more than public safety)
Adding these together gives us a total of B/4 + 3B/8 + B/4. Converting to a common denominator, we get 2B/8 + 3B/8 + 2B/8 = 7B/8. Therefore, 1 - 7B/8 = B/8 of the budget is left for other expenses.