Answer:
40, 24, 54
Step-by-step explanation:
let the 3 numbers be x, y and z
then
[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )
5y = 3x ( divide both sides by 5 )
y = [tex]\frac{3}{5}[/tex] x
and
[tex]\frac{y}{z}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )
4z = 9y ( divide both sides by 4 )
z = [tex]\frac{9}{4}[/tex] y = [tex]\frac{9}{4}[/tex] × [tex]\frac{3}{5}[/tex] x = [tex]\frac{27}{20}[/tex] x
The 3 numbers are now expressed in terms of x , then adding gives
x + [tex]\frac{3}{5}[/tex] x + [tex]\frac{27}{20}[/tex] x = 118
multiply through by 20 to clear the fractions
20x + 12x + 27x = 2360
59x = 2360 ( divide both sides by 59 )
x = 40 ← first number
y = [tex]\frac{3}{5}[/tex] × 40 = 3 × 8 = 24 ← second number
z = [tex]\frac{27}{20}[/tex] × 40 = 27 × 2 = 54 ← third number
The 3 numbers are 40, 24, 54
