Question

A+b+c=24.
30a=40b=24c

Answer 1

`30a=24c\ \ \ \ \ |:30\\\\a=(24)/(30)c\\\\a=(4)/(5)c\\\\40b=\dfrc{24}{c}\ \ \ \ |:40\\\\b=(24)/(40)c\\\\b=(3)/(5)c`

substitute to a + b + c = 24

`(4)/(5)c+(3)/(5)c+c=24\ \ \ \ |\cdot5\\\\4c+3c+5c=120\\\\12c=120\ \ \ |:12\\\\\boxed{c=10}\\\\a=(4)/(5)c\to a=(4)/(5)\cdot10=\to\boxed{a=8}\\\\b=(3)/(5)c\to b=(3)/(5)\cdot10\to\boxed{b=6}`