1. **State the problem:** There are two candidates in an election who received 51% and 26% of the total electorate's votes respectively. Additionally, 4600 voters did not vote. We need to find the total number of voters who voted. 2. **Define variables:** Let the total number of voters in the electorate be $T$. 3. **Express the votes:** Votes for candidate 1 = $0.51T$, votes for candidate 2 = $0.26T$, and non-voters = 4600. 4. **Formulate the equation:** Since the total electorate is the sum of voters who voted and those who did not vote, we have: $$0.51T + 0.26T + 4600 = T$$ 5. **Simplify the equation:** $$0.77T + 4600 = T$$ 6. **Isolate $T$:** $$T - 0.77T = 4600$$ $$0.23T = 4600$$ 7. **Solve for $T$:** $$T = \frac{4600}{0.23} = 20000$$ 8. **Find total voters who voted:** $$\text{Voted} = 0.51T + 0.26T = 0.77T = 0.77 \times 20000 = 15400$$ **Final answer:** 15400 voters voted in all.