Question

The ratio of the number of boys to the number of girls at school is 7:8. There are 330 students at this school. For each of the following statements, explain whether the statement is true or false and why: The number of girls at school is 7/8 the number of boys. 7/8 of the students in the school are girls. There are exactly 22 more girls than boys. There are exactly 176 boys at the school. 8/15 of the students in the school are girls.

Answer 1

$\huge\bold{\gray{\sf{Given:}}}$

Ratio of number of boys to the number of girls at school is 7:8.

Total number of students in the school =330

$\huge\bold{\gray{\sf{To\:Find:}}}$

The number of boys and girls in the school

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

Explanation:

Ratio of boys and girls =7:8

Let the boys be 7x

and girls be 8x

According to the question:-

$= > 7x + 8x = 330$

$= > 15x = 330$

$= > x = \frac{330}{15} = \frac{66}{3} = 22$

• $\bold{\red{Boys}}=154$
• $\bold{\red{Girls}}=176$

The number of boys in the school =7x=7×22=154

Number of girls in the school=8×22=176

Check:154+176=330

The above all statement is true let's check:-

• The number of girls at school is 7/8 the number of boys.

$= > \frac{7}{8} \times 176 = 22 \times 7 = 154$

• There are exactly 22 more girls than boys.

$= > 154 + 22 = 176(girls)$

• There are exactly 176 girls in the school.

• 8/15 of the students in the school are girls.

$= > \frac{8}{15} \times 330 = 22 \times 8 = 176(girls)$