Question

4a-5b:5a+4b=1:3 then find the value of a:b​

Answer 1

Explanation:

4a-5b:5a+4b=1:3

4a-5b/5a+4b=1:3cross multiply

3(4a-5b)=1(5a+4b)

12a-15b=5a+4b

Collect like terms

12a-5a=4b+15b

7a=19b

a:b=7:19

Answer 2

a : b = 19 : 7

Explanation:

Given

4a - 5b : 5a + 4b = 1 : 3

Expressing in fractional form, that is

`(4a-5b)/(5a+4b)` =
`(1)/(3)` ( 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 =
`(19)/(7)` b ( divide both sides by b )

`(a)/(b)` =
`(19)/(7)`

That is a : b = 19 : 7