On May $31$ Partner Gambit buys $10\%$ of partner Wolverine's interest in the equal DW calendar$-$year partnership, so Gambit owns $10\%$ and Wolverine owns $40\%$ after the sale. For the year, the partnership earns income of $$7,000$ a month for January through July, and $$12,000$ a month for August through December. How much income will Wolverine and Gambit each have from the partnership under $($a$)$ the interim closing method and $($b$)$ the proration of partnership income method?