Problem $08\mathrm{.}012-$ Calculating rate of return given multiple alternative

ZipCar auto parts store has $$100,000$ to invest in a project to detect and redice insier theft in their stores. They are considering investing in one of two alternatives, identified as $Y$ and $Z.Z$ is the higher first$-$cost alternative, and the incremental initial investment between the two is $$58\mathrm{.}000$ and will exhibit a rate of return of $12\mathrm{.}00\%$ per year. $Z$ requires an irvestment of $$100,000.$ They expect a rate of return on the $$100,000$ investment of $37,00$ percent. Answer the following questions; $($a$)$ what is the size of the investment required in $Y?,$ and $($b$)$ what is the rate of return on $Y?$

The size of the investment required in $Y$ is $

The rate of return on $Y$ is $\%.($Round the final answer to three decimal places.$)$