# Garden Variety Family

Some siblings* were discussing the unique mathematical qualities of their respective ages the other day, and they determined that at one point in history, the following equations were true.

$$\hskip 2.7 in a = b * c$$
$$\hskip 2.7 in a = b * 2$$
$$\hskip 2.7 in c = b * 4$$
$$\hskip 2.7 in c - b = 0$$
$$\hskip 2.7 in d = e * f$$
$$\hskip 2.7 in d = e * 3$$
$$\hskip 2.7 in f = e * 7$$
$$\hskip 2.7 in g = f * 2$$
$$\hskip 2.7 in g = h * 1$$
$$\hskip 2.7 in g = e + f$$

Numbers are "age in years" rounded to the nearest whole number age, and each letter variable is representative of an individual sibling's age.

Now, the question to you is:

## What is their mother's unfortunate nickname?

* Human siblings

• @athin I recently saw this interview in which she talks about how she hates the nickname, and I genuinely feel bad that she (and her children) have been burdened by it. – Chowzen Nov 23 '18 at 11:18
• Riddles should be clever and creative. Riddles that are too easy or unimaginative are not fun to solve, although it is hard to draw a line here since difficulty is very subjective. In addition, riddles with crucial details omitted can frustrate solvers. – JonMark Perry Nov 23 '18 at 12:12
• A quote from Rand al'Thor from puzzling.meta.stackexchange.com/questions/3142/… – JonMark Perry Nov 23 '18 at 12:13

They were all born at the same time since each equation holds true if $$a=b=c=d=e=f=g=h$$