Question

If a: b = 2:3, b: c = 4:3, and c: d = 7: 8, find a: d.

Answer 1

a:d=7:9

Explanation:

We have a system with 3 equation:

`(a)/(b)=(2)/(3)\\(b)/(c)=(4)/(3)\\(c)/(d)=(7)/(8)`

If we multiply all of these equations, then we have:

`(a)/(b)*(b)/(c)*(c)/(d)=(2)/(3)*(4)/(3)*(7)/(8)\\(a*b*c)/(b*c*d)=(2*4*7)/(3*3*8)\\(a)/(d)=(56)/(72)`

If we simplify this fraction dividing by 9, then:

`(a)/(d)=(56:9)/(72:9)=(7)/(9)`

Therefore, a:d=7:9