Matthew, Incorporated, owns $30$ percent of the outstanding stock of Lindman Company and has the ability to significantly influence the investee's operations and decision making. On January $1,2024,$ the balance in the Investment in Lindman account is $$433,000.$

Amortization associated with this acquisition is $$18,800$ per year. In $2024,$ Lindman earns an income of $$91,000$ and declares cash dividends of $$45,500.$ Previously, in $2023,$ Lindman had sold inventory costing $$27,000$ to Matthew for $$45,000.$ Matthew consumed all but $25$ percent of this merchandise during $2023$ and used the ret during $2024.$ Lindman sold additional inventory costing $$36,400$ to Matthew for $$65,000$ in $2024.$ Matthew did not consume $40$ percent of these $2024$ purchases from Lindman until $2025.$a$.$ What amount of equity method income would Matthew recognize in $2024$ from its ownership interest in Lindman?

b$.$ What is the equity method balance in the Investment in Lindman account at the end of $2024?$