A city spent about 1/4 of its budget on buildings and maintenance, which was about 1/8 of the total budget less than it spent on administrative personnel. The amount spent on administrative personnel was about 1/8 of the budget more than was spent on public safety. About what part of the budget was left for other expenses?

Question

Mathematics

Simon Hinton

9 August, 13:17

A city spent about 1/4 of its budget on buildings and maintenance, which was about 1/8 of the total budget less than it spent on administrative personnel. The amount spent on administrative personnel was about 1/8 of the budget more than was spent on public safety. About what part of the budget was left for other expenses?

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Munchkin · Answer 1

1/8 of the budget was left for other expenses.

Step-by-step explanation:

1/4 of the budget - buildings and maintenance.

Administrative personnel : 1/4 + 1/8 = 2/8 + 1/8 = 3/8 of the budget.

Therefore:

3/8 of the budget - administrative personnel.

Public safety : 3/8 - 1/8 = 2/8 = 1/4 of the budget.

For other expenses:

1 - (1/4 + 3/8 + 1/4) = 1 - (2/8 + 3/8 + 2/8) 1 - 7/8 = 1/8

Finally, 1/8 of the total budget was for the other expenses.