1. Problem: Solve for the missing value in each case from 10 to 24. 2. Formula: To find a percentage of a number, use the formula $$\text{Percentage value} = \frac{x}{100} \times \text{Total}$$ where $x$ is the percentage. 3. Important rules: - To find $x$% of a number, multiply the number by $\frac{x}{100}$. - To find what percentage $x$ is of a number, use $x = \frac{\text{part}}{\text{whole}} \times 100$. - To find the whole when given a part and percentage, use $\text{whole} = \frac{\text{part} \times 100}{x}$. 4. Solve each: 10. $x\%$ of 64 is 10 $$\frac{x}{100} \times 64 = 10$$ $$64 \times \frac{x}{100} = 10$$ $$\cancel{64} \times \frac{x}{100} = 10$$ $$x = \frac{10 \times 100}{64} = \frac{1000}{64} = 15.625$$ 11. $x$ is 45% of 96 $$x = \frac{45}{100} \times 96 = 0.45 \times 96 = 43.2$$ 12. 33% of 80 is $x$ $$x = \frac{33}{100} \times 80 = 0.33 \times 80 = 26.4$$ 13. 16 is $x$% of 104 $$\frac{x}{100} \times 104 = 16$$ $$104 \times \frac{x}{100} = 16$$ $$\cancel{104} \times \frac{x}{100} = 16$$ $$x = \frac{16 \times 100}{104} = \frac{1600}{104} \approx 15.38$$ 14. $x$% of 46 is 276 $$\frac{x}{100} \times 46 = 276$$ $$46 \times \frac{x}{100} = 276$$ $$\cancel{46} \times \frac{x}{100} = 276$$ $$x = \frac{276 \times 100}{46} = \frac{27600}{46} = 600$$ 15. $x$% of 30 is 20 $$\frac{x}{100} \times 30 = 20$$ $$30 \times \frac{x}{100} = 20$$ $$\cancel{30} \times \frac{x}{100} = 20$$ $$x = \frac{20 \times 100}{30} = \frac{2000}{30} \approx 66.67$$ 16. 9 is 30% of what? $$9 = \frac{30}{100} \times \text{whole}$$ $$9 = 0.3 \times \text{whole}$$ $$\text{whole} = \frac{9}{0.3} = 30$$ 17. 210% of $y$ is 3150 $$\frac{210}{100} \times y = 3150$$ $$2.1y = 3150$$ $$y = \frac{3150}{2.1} = 1500$$ 18. 50.5% of 80 is $c$ $$c = \frac{50.5}{100} \times 80 = 0.505 \times 80 = 40.4$$ 19. $m$ is 7.5% of 64 $$m = \frac{7.5}{100} \times 64 = 0.075 \times 64 = 4.8$$ 20. 80 is 60% of $k$ $$80 = \frac{60}{100} \times k$$ $$80 = 0.6k$$ $$k = \frac{80}{0.6} = 133.33$$ 21. $z$ is 8% of 64 $$z = \frac{8}{100} \times 64 = 0.08 \times 64 = 5.12$$ 22. $s$ is 112% of 150 $$s = \frac{112}{100} \times 150 = 1.12 \times 150 = 168$$ 23. $r$% of 12.8 is 11.2 $$\frac{r}{100} \times 12.8 = 11.2$$ $$12.8 \times \frac{r}{100} = 11.2$$ $$\cancel{12.8} \times \frac{r}{100} = 11.2$$ $$r = \frac{11.2 \times 100}{12.8} = \frac{1120}{12.8} = 87.5$$ 24. 180% of 125 is $y$ $$y = \frac{180}{100} \times 125 = 1.8 \times 125 = 225$$ Final answers: 10. 15.625 11. 43.2 12. 26.4 13. 15.38 14. 600 15. 66.67 16. 30 17. 1500 18. 40.4 19. 4.8 20. 133.33 21. 5.12 22. 168 23. 87.5 24. 225