Please, help me with this problem. Could you explain it step by step?

You own your own firm, and you want to raise $30 million to fund an expansion. Currently, you won 100% of the firm's equity, and the firm has no debt. To raise the 30 million solely though equity, you will need to sell two-thirds of the firm. However, you would prefer to maintain at least a 50% equity stake in the firm to retain control. 1) If you borrow $20 million, what fraction of the equity will you need to sell to raise the remaining S10 million? (Assume perfect capital markets.) 2) What is the smallest amount you can borrow to raise the $30 million without giving up control? (Assume perfect capital market.)