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

ZipCar auto parts store has $$84,000$ to invest in a project to detect and reduce insier theft in their stores. They are considering investing in one of two alternatives, identified as Y and Z$.$ Z is the higher first$-$cost alternative, and the incremental initial investment between the two is $$54,000$ and will exhibit a rate of return of $8\mathrm{.}00\%$ per year. Z requires an investment of $$84,000.$ They expect a rate of return on the $$84,000$ investment of $49\mathrm{.}00$ 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$?$

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

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