Given:
Number of boys = [tex]\dfrac{1}{4}[/tex] of the total persons.
Number of girls = [tex]\dfrac{5}{8}[/tex] of the total persons.
Remaining persons are adults.
There were 56 more girls than adults.
To find:
The number of total persons.
Solution:
Let x be the number of total persons. Then,
Number of boys = [tex]\dfrac{1}{4}x[/tex]
Number of girls = [tex]\dfrac{5}{8}x[/tex]
Number of adults = Total persons - Boys - Girls
= [tex]x-\dfrac{1}{4}x-\dfrac{5}{8}x[/tex]
= [tex]\dfrac{8x-2x-5x}{8}[/tex]
= [tex]\dfrac{x}{8}[/tex]
There were 56 more girls than adults.
Girls = Adults + 56
[tex]\dfrac{5}{8}x=\dfrac{x}{8}+56[/tex]
[tex]\dfrac{5}{8}x-\dfrac{x}{8}=56[/tex]
[tex]\dfrac{4}{8}x=56[/tex]
[tex]\dfrac{1}{2}x=56[/tex]
Multiply both sides by 2.
[tex]x=112[/tex]
Therefore, the total number of persons is 112.
