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

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

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
`*` 30 = 120

And, number of girls = 5
`*` 30 = 150

As per Statement 1:

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

`(4)/(5)* 150 = 4 * 30 = 120` = Number of boys.

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

`(4)/(9)* 270= 4 * 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.