if b is two thirds of c. 5a = 4c Work out the ratio a : b : c

So firstly, we need to write the statement "b is two thirds of c" as an equation. This can be written as b=2/3 c. As a ratio this can be written as b:c is 2/3:1 . Now we went to write the equation 5a=4c in such a way that we can make a ratio where c has the coefficient of 1. This can be done by dividing both sides by 5, a=4/5 c. This means the ratio a:c is 4/5:1. We can merge the b:c and a:c ratios we worked as the coefficient of c is equal on both, therefore a:b:c, 4/5:2/3:1. We can leave the answer like this or tidy it up by getting rid of the fractions . To do this we multiply all numbers by 5, resulting in 4:10/3:5, and then we multiply all the numbers by 3 which gives us 12:10:15.