I2.2 Let $a, b$ and $c$ be real numbers with ratios $b:(a+c)=1: 2$ and $a:(b+c)=1: P$.
If $Q=\frac{a+b+c}{a}$, find the value of $Q$.
$$
2 b=a+c \ldots \ldots
$$
(1), $3 a=b+c$
(1) - (2): $2 b-3 a=a-b \Rightarrow 3 b=4 a \Rightarrow a: b=3: 4$

Let $a=3 k, b=4 k$, sub. into (1): $2(4 k)=3 k+c \Rightarrow c=5 k$
$$
Q=\frac{a+b+c}{a}=\frac{3 k+4 k+5 k}{3 k}=4
$$