If FG = 4, GH = 8x, and FH = 10x, what is FH?

Step-by-step solution

1. 1

   Set up the addition relation. With $G$ between $F$ and $H$:

   $FG+GH=FH\;\Longrightarrow\;4+8x=10x$

   Here two of the three lengths carry the variable, so the lone constant term is what pins $x$ down.

2. 2

   Collect the $x$ terms. Subtract $8x$ from both sides:

   $4=10x-8x=2x\;\Longrightarrow\;x=2$

3. 3

   Compute the requested whole segment.

   $FH=10x=10(2)=20$

4. 4

   Break the whole into its parts and check. $FG=4$ and $GH=8(2)=16$, so

   $4+16=20=FH\;\checkmark$

   The proportions are consistent with the coefficients: $GH$ takes $\tfrac{8}{10}=80\%$ of the whole and $FG$ the remaining $20\%$, which is exactly $4$ out of $20$.