If the liabilities of a business increased $83,000 during a period of time and the stockholders' equity in the business decreased $34,000 during the same period, the assets of the business must have:

The assets of the business must have increased by $49,000.

Explanation:

Every time when a change in any type of account occur it should satisfy the accounting equation as follow:

Asset = Equity + Liabilities

So, the same situation is

Change in Asset = Change in Equity + Change in Liabilities

Change in Asset = - $34,000 + $83,000

Change in Asset = $49,000

So, the net change in the assets will be $49,000. This value is the net of change in the assets section resulting the change due to Equity and liability transaction.