1. **State the problem:** Mrs. Mary Moolah invested a total of $20,000 in two types of bonds. One bond pays 5% interest, and the other pays 8%. The total interest earned from both investments is $1,150. We need to find how much was invested at the 5% rate. 2. **Define variables:** Let $x$ be the amount invested at 5% interest. Then the amount invested at 8% is $20000 - x$. 3. **Write the equation for total interest:** The interest from the 5% investment is $0.05x$, and from the 8% investment is $0.08(20000 - x)$. The total interest is given as $1150$, so: $$0.05x + 0.08(20000 - x) = 1150$$ 4. **Expand and simplify:** $$0.05x + 0.08 \times 20000 - 0.08x = 1150$$ $$0.05x + 1600 - 0.08x = 1150$$ 5. **Combine like terms:** $$0.05x - 0.08x + 1600 = 1150$$ $$-0.03x + 1600 = 1150$$ 6. **Isolate $x$:** $$-0.03x = 1150 - 1600$$ $$-0.03x = -450$$ 7. **Divide both sides by $-0.03$:** $$x = \frac{-450}{\cancel{-0.03}} \cancel{-} = \frac{450}{0.03}$$ 8. **Calculate $x$:** $$x = 15000$$ **Answer:** Mrs. Mary Moolah invested $15000 at the 5% interest rate.