Question

The ratio of the number of boys to the number of girls at Liam's school is 4:5. There are 270 students at his school. Statement 1: The number of boys at school is 4/5 the number of girls.

Answer 1

Answer:

"statement 1: The number of boys at the school is $\frac{4}5$ of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = $4x$

Let, Number of girls = $5x$

Total number of students = Number of boys + Number of girls = 270

$\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}$

Therefore, number of boys = 4 $\times$ 30 = 120

And, number of girls = 5 $\times$ 30 = 150

As per Statement 1:

Finding $\frac{4}5$ of the number of girls:

$\dfrac{4}{5}\times 150 = 4 \times 30 = 120$ = Number of boys.

Finding $\frac{4}9$ of the total number of students:

$\frac{4}{9}\times 270= 4 \times 30 = 120$ = Number of boys.

Number of boys is equal to $\frac{4}9$ of total number of students.

So, "statement 1: The number of boys at the school is $\frac{4}5$ of the number of girls." is true.