A company makes all purchases on account, subject to the following payment pattern.

Paid in the month of purchase: $30\%$

Paid in the first month following purchase: $65\%$

Paid in the second month following purchase: $5\%$

If purchases for April, May, and June were $$200,000,$$$160,000,$ and $$250,000,$ respectively, what was the firm's budgeted payables balance on May $31?$

a$.$ $$118,000$

b$.$ $$122,000$

c$.$ $$178,000$

d$.$ $$126,000$