Answer:
"statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] 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 = [tex]4x[/tex]
Let, Number of girls = [tex]5x[/tex]
Total number of students = Number of boys + Number of girls = 270
[tex]\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}[/tex]
Therefore, number of boys = 4 [tex]\times[/tex] 30 = 120
And, number of girls = 5 [tex]\times[/tex] 30 = 150
As per Statement 1:
Finding [tex]\frac{4}5[/tex] of the number of girls:
[tex]\dfrac{4}{5}\times 150 = 4 \times 30 = 120[/tex] = Number of boys.
Finding [tex]\frac{4}9[/tex] of the total number of students:
[tex]\frac{4}{9}\times 270= 4 \times 30 = 120[/tex] = Number of boys.
Number of boys is equal to [tex]\frac{4}9[/tex] of total number of students.
So, "statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.
