Dividing Numbers Into Rations

Question

The question is:

Suppose $60$ is divided into $3$ parts in the ratio of $1$:$3$:$6$. What is the value of the middle part?

I tried to take $60$, divide it into $3$ parts and divide those $3$ parts accordingly to $1$:$3$:$6$, and I got $30$. This is obviously wrong, so can someone point me in the right direction?

Answer 1

Hint: If the smallest part is $x$, the next is $3x$ and the last is $6x$. These all add up to $60$

Answer 2

We have $$x:3x:6x$$ and the sum must be $60$, so $$x+3x+6x=60\Longrightarrow 10x=60\Longrightarrow x=6$$

Answer 3

You should calculate $1+3+6=10$

and then find $\dfrac{1}{10},\dfrac{3}{10},\dfrac{6}{10}$ of $60$

to give $6:18:36$.

Answer 4

Say the parts are $a,b$ and $c$, then we know that $a:b=1:3$, so $a=\frac 1 3 b$ and $b:c=3:6=1:2$ so $c=2b$, so $$a+b+c=\frac 1 3 b+b+2b=60$$ now, can you calculate $b$?