In a secondary school of 800 students, 45\% of the students are girls. If \frac{1}{6} of t… — JAMB UTME

In a secondary school of $800$ students, $45\%$ of the students are girls. If $\frac{1}{6}$ of the girls and $\frac{1}{4}$ of the boys wear eyeglasses, what is the total number of students in the school who wear eyeglasses?

Answer: 170 students

Answer

170 students

Calculating

45\%

800

gives

360

girls, leaving

800 - 360 = 440

boys. Taking

\frac{1}{6}

360

gives

60

girls with eyeglasses, and taking

\frac{1}{4}

440

gives

110

boys with eyeglasses. Adding these two quantities yields

60 + 110 = 170

students.

Step-by-Step Solution

Find the total number of girls

360 girls

45% of the total 800 students are girls

Find the total number of boys

440 boys

Subtracting the number of girls (360) from total students (800) gives the number of boys

Find the number of girls wearing eyeglasses

60 girls

One-sixth of the 360 girls wear eyeglasses

Find the number of boys wearing eyeglasses

110 boys

One-fourth of the 440 boys wear eyeglasses

Sum the girls and boys wearing eyeglasses

170 students

Adding 60 girls and 110 boys gives the total students wearing eyeglasses

Key Concept

Fractions and Percentages of Quantities

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