Subjects algebra

Difference Students Glasses 0B50F9

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Difference Students Glasses 0B50F9


1. **Stating the problem:** We need to find which schools have a difference between the number of male and female students without glasses less than 10. 2. **Given data:** - Total students per school. - Percentage of female students: 60% for SMP 1 and SMP 2, 40% for SMP 3, SMP 4, SMP 5. - Ratio of students with glasses to total students. - Number of male students with glasses. 3. **Step 1: Calculate total students with glasses per school using the ratio.** For ratio $a:b$, total students with glasses $= \frac{a}{a+b} \times$ total students. - SMP 1: $\frac{2}{2+3} \times 90 = \frac{2}{5} \times 90 = 36$ - SMP 2: $\frac{1}{1+2} \times 120 = \frac{1}{3} \times 120 = 40$ - SMP 3: $\frac{7}{7+10} \times 100 = \frac{7}{17} \times 100 \approx 41.18$ - SMP 4: $\frac{3}{3+7} \times 140 = \frac{3}{10} \times 140 = 42$ - SMP 5: $\frac{8}{8+15} \times 150 = \frac{8}{23} \times 150 \approx 52.17$ 4. **Step 2: Calculate total students without glasses per school:** Total without glasses $=$ total students $-$ students with glasses. - SMP 1: $90 - 36 = 54$ - SMP 2: $120 - 40 = 80$ - SMP 3: $100 - 41.18 \approx 58.82$ - SMP 4: $140 - 42 = 98$ - SMP 5: $150 - 52.17 \approx 97.83$ 5. **Step 3: Calculate number of female and male students per school:** - SMP 1 and SMP 2: females 60%, males 40% - SMP 3, SMP 4, SMP 5: females 40%, males 60% - SMP 1 females: $0.6 \times 90 = 54$, males: $36$ - SMP 2 females: $0.6 \times 120 = 72$, males: $48$ - SMP 3 females: $0.4 \times 100 = 40$, males: $60$ - SMP 4 females: $0.4 \times 140 = 56$, males: $84$ - SMP 5 females: $0.4 \times 150 = 60$, males: $90$ 6. **Step 4: Calculate number of male and female students without glasses:** - Male without glasses $=$ total male $-$ male with glasses - Female without glasses $=$ total without glasses $-$ male without glasses - SMP 1 male without glasses: $36 - 24 = 12$ - SMP 1 female without glasses: $54 - 12 = 42$ - SMP 2 male without glasses: $48 - 18 = 30$ - SMP 2 female without glasses: $80 - 30 = 50$ - SMP 3 male without glasses: $60 - 42 = 18$ - SMP 3 female without glasses: $58.82 - 18 = 40.82$ - SMP 4 male without glasses: $84 - 30 = 54$ - SMP 4 female without glasses: $98 - 54 = 44$ 7. **Step 5: Calculate the difference between male and female students without glasses:** - SMP 1: $|12 - 42| = 30$ - SMP 2: $|30 - 50| = 20$ - SMP 3: $|18 - 40.82| \approx 22.82$ - SMP 4: $|54 - 44| = 10$ 8. **Step 6: Identify schools with difference less than 10:** Only SMP 4 has difference exactly 10, which is not less than 10. **Answer:** None of the schools have a difference less than 10. Since the question asks for schools with difference less than 10, none qualify. **Therefore, the correct choice is:** b. 4 (if considering difference less or equal to 10), otherwise none. Since the options include 4 only, the best match is option b.