Answer:
a : b = 19 : 7
Step-by-step explanation:
Given
4a - 5b : 5a + 4b = 1 : 3
Expressing in fractional form, that is
[tex]\frac{4a-5b}{5a+4b}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3(4a - 5b) = 5a + 4b ← distribute left side
12a - 15b = 5a + 4b ( subtract 5a from both sides )
7a - 15b = 4b ( add 15b to both sides )
7a = 19b ( divide both sides by 7 )
a = [tex]\frac{19}{7}[/tex] b ( divide both sides by b )
[tex]\frac{a}{b}[/tex] = [tex]\frac{19}{7}[/tex]
That is a : b = 19 : 7
