Question

Question 25 Given that a: b = 8:5 and b: c = 3:4, find the ratio a: b: c Give your answer in its simplest form.​

Answer 1

24 : 15 : 20

Explanation:

express ratios in fractional form and express b and c in terms of a

`(a)/(b)` =
`(8)/(5)` ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b =
`(5)/(8)` a

also

`(b)/(c)` =
`(3)/(4)` ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c =
`(4)/(3)` b =
`(4)/(3)` ×
`(5)/(8)` a =
`(5)/(6)` a

Then

a : b : c

= a :
`(5)/(8)` a :
`(5)/(6)` a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form