Saly and Jena formed a partnership with capital contributions of $300,000 and $400,000, respectively. Their partnership agreement calls dividing net income or loss in a fixed ratio of 1: 2, respectively. Rita is to join the partnership, by investing an amount of cash. After Rita's admission, Saly's capital became $290,000. If Rita's capital account was credited for $350,000 when she joined, determine the amount of cash invested by Rita in the firm.