Assume that the City of Coyote has produced its financial statements for December $31,2024,$ and the year then ended. The city$$s general fund was only used to monitor education and parks. Its capital projects funds worked in connection with each of these functions at times during the current year. The city also maintained an enterprise fund to account for its art museum.

The government$-$wide financial statements provide the following figures:

Education reports net expenses of $$736,000.$

Parks reports net expenses of $$179,000.$

Art museum reports net revenues of $$68,750.$

General government revenues for the year were $$1,048,250$ with an overall increase in the city's net position of $$202,000.$

The fund financial statements provide the following for the entire year:

The general fund reports a $$39,250$ increase in its fund balance.

The capital projects fund reports a $$61,000$ increase in its fund balance.

The enterprise fund reports a $$82,250$ increase in its net position.

The city asks the CPA firm of Abernethy and Chapman to examine several transactions that occurred during $2024$ and indicate how to correct any erroneous reporting. Officials also want to know the effect of each error. View each of the following situations as independent.

In $2024,$ the City of Coyote receives a $$560,000$ cash grant from the state to reduce air pollution. Although a special revenue fund could have been set up$,$ the money remains in the general fund. The cash was received immediately but will have to be returned if the city does not lower its air pollution by $25$ percent by $2028.$ On December $31,2024,$ Coyote spends $$380,000$ of the money for a large machine to help begin the process of reducing air pollution. City officials expect the machine to last for five years. The city recorded the cost as an expenditure in the general fund but as an asset on the government$-$wide financial statements, where it was depreciated based on the straight$-$line method and the half$-$year convention. Because the city received the money, it recorded all $$560,000$ as a revenue on both the fund and the government$-$wide financial statements.

Required:

What was the correct change for $2024$ in the total fund balance reported by the general fund?

What was the correct overall change in the net position reported on the government$-$wide financial statements?Required:

a$.$ What was the correct change for $2024$ in the total fund balance reported by the general fund?

b$.$ What was the correct overall change in the net position reported on the government$-$wide financial statements?