1. **State the problem:** Rebecca must give 5 out of every 6 dollars she earns to the tax department. She keeps the remaining amount. This week, she kept 10 dollars. We need to find out how much she earned in total this week. 2. **Define variables:** Let $x$ be the total amount Rebecca earned this week. 3. **Set up the equation:** Since she gives 5 out of every 6 dollars to tax, she keeps $\frac{1}{6}$ of her total earnings. 4. **Write the equation:** The amount she keeps is $\frac{1}{6}x$, and we know this equals 10 dollars. $$\frac{1}{6}x = 10$$ 5. **Solve for $x$:** Multiply both sides by 6 to isolate $x$: $$x = 10 \times 6$$ $$x = 60$$ 6. **Interpret the result:** Rebecca earned 60 dollars in total this week. **Final answer:** $60$ dollars.