1. **Problem 6:** The sixth, seventh, and eighth grades raised money for their middle school. The sixth grade raised 40% of the total, the seventh grade raised 22%, and the eighth grade raised the rest. The eighth grade raised 1368. Find the total amount raised. 2. **Formula and rules:** - Total percentage must add up to 100%. - If $x$ is the total amount raised, then the eighth grade raised $(100\%-40\%-22\%)x = 38\%x$. - We know $38\%x = 1368$. 3. **Calculation:** $$0.38x = 1368$$ Divide both sides by 0.38: $$x = \frac{1368}{0.38}$$ $$x = 3600$$ 4. **Answer for problem 6:** The total amount raised by the three grades is 3600. --- 5. **Problem 7:** Yuna and Scott ran for sixth-grade class president. Yuna received 45% of the votes. Scott received 18 more votes than Yuna. Find how many votes Scott received. 6. **Formula and rules:** - Let total votes be $V$. - Yuna's votes: $0.45V$. - Scott's votes: $0.45V + 18$. - Since only Yuna and Scott ran, their votes add to total votes: $$0.45V + (0.45V + 18) = V$$ 7. **Calculation:** $$0.9V + 18 = V$$ Subtract $0.9V$ from both sides: $$18 = V - 0.9V = 0.1V$$ Divide both sides by 0.1: $$V = \frac{18}{0.1} = 180$$ 8. Scott's votes: $$0.45V + 18 = 0.45 \times 180 + 18 = 81 + 18 = 99$$ 9. **Answer for problem 7:** Scott received 99 votes.