x - male lions
y - female lions
The ratio of the number of male lions to female lions is 21:20.
[tex]\frac{x}{y}=\frac{21}{20} \\ x=\frac{21}{20}y[/tex]
There are 123 lions.
[tex]x+y=123 \\
x=123-y[/tex]
Set both equations equal to each other:
[tex]x=x \\
\frac{21}{20}y=123-y \ \ \ |+y \\
\frac{21}{20}y+y=123 \ \ \ |\times 20 \\
21y+20y=2460 \\
41y=2460 \ \ \ |\div 41 \\
y=60[/tex]
There are 60 female lions.
