Question

B is two fifths of c 4a = 3c work out the ratio a:b:c give your answer in its simplest form where a, b and c are integers

Answer 1

Answer:

a : b : c = 12 : 10 : 15

Step-by-step explanation:

Given that: b = $\frac{2}{5}$ of c

 i.e             b = $\frac{2c}{5}$ ............... 1

          2c = 5b

So that;

          c = $\frac{5b}{2}$ .................... 2

Also,    

          4a = 3c

           a = $\frac{3c}{4}$ ................ 3

⇒          a = $\frac{3}{4}$ × ($\frac{5b}{2}$)

             a = $\frac{15b}{8}$ ................. 4

           15b = 8a

           b = $\frac{8a}{15}$ ................. 5

Comparing the derived equations:

From equations 2 and 3,

a:c = $\frac{15b}{8}$: $\frac{5b}{2}$ = 4:5

From equations 1 and 2,

b:c = $\frac{2c}{5}$ : $\frac{5b}{2}$ = 2:3

But a common value of b = 15, gives;

a : c = 12 : 15 and b : c = 10 : 15  

Thus, a : b : c = 12 : 10 : 15