Answer:
A : C = 2 : 1
Step-by-step explanation:
Expressing the ratios in fractional form
[tex]\frac{2A}{3B}[/tex] = [tex]\frac{5}{6}[/tex] ( cross- multiply )
15B = 12A ( divide both sides by 15 )
B = [tex]\frac{12}{15}[/tex] A = [tex]\frac{4}{5}[/tex] A
and
[tex]\frac{3B}{2C}[/tex] = [tex]\frac{36}{15}[/tex] ( cross- multiply )
45B = 72C ( substitute B = [tex]\frac{4}{5}[/tex] A )
45 × [tex]\frac{4}{5}[/tex] A = 72C
36A = 72C ( divide both sides by C )
36 × [tex]\frac{A}{C}[/tex] = 72 ( divide both sides by 36 )
[tex]\frac{A}{C}[/tex] = [tex]\frac{72}{36}[/tex] = [tex]\frac{2}{1}[/tex]
Then
A : C = 2 : 1
