1. **State the problem:** Jamelia and Shahzad earn a combined salary of 110000. If Jamelia's salary is cut in half and Shahzad's salary is doubled, their total salary becomes 115000. Find each of their salaries. 2. **Define variables:** Let $J$ be Jamelia's salary and $S$ be Shahzad's salary. 3. **Write the system of equations:** \begin{align*} J + S &= 110000 \\ \frac{J}{2} + 2S &= 115000 \end{align*} 4. **Use substitution or elimination. Here, use substitution:** From the first equation, solve for $J$: $$J = 110000 - S$$ 5. **Substitute $J$ into the second equation:** $$\frac{110000 - S}{2} + 2S = 115000$$ 6. **Multiply both sides by 2 to clear the denominator:** $$\cancel{2} \times \left(\frac{110000 - S}{\cancel{2}} + 2S\right) = 2 \times 115000$$ $$110000 - S + 4S = 230000$$ 7. **Simplify:** $$110000 + 3S = 230000$$ 8. **Isolate $S$:** $$3S = 230000 - 110000$$ $$3S = 120000$$ 9. **Divide both sides by 3:** $$\cancel{3}S = \frac{120000}{\cancel{3}}$$ $$S = 40000$$ 10. **Find $J$ using $J = 110000 - S$:** $$J = 110000 - 40000 = 70000$$ **Final answer:** Jamelia's salary is $70000$ and Shahzad's salary is $40000$.