HMMT November 2017 H3

Emilia wishes to create a basic solution with $7 \%$ hydroxide $(\mathrm{OH})$ ions. She has three solutions of different bases available: $10 \%$ rubidium hydroxide $(\mathrm{Rb}(\mathrm{OH})), 8 \%$ cesium hydroxide $(\mathrm{Cs}(\mathrm{OH}))$, and $5 \%$ francium hydroxide $(\mathrm{Fr}(\mathrm{OH})$ ). ( $\mathrm{The} \mathrm{Rb}(\mathrm{OH})$ solution has both $10 \% \mathrm{Rb}$ ions and $10 \% \mathrm{OH}$ ions, and similar for the other solutions.) Since francium is highly radioactive, its concentration in the final solution should not exceed $2 \%$. What is the highest possible concentration of rubidium in her solution?