Question

Fred is 58 yes old, and Irene is 18. How many years ago was Fred 5 times as old as Irene. Algebra must be used

Answer 1

So let's take a peek at both's ages, keep in mind, every year, is 1year added to Irene and 1year added to Fred
so... if we look at their ages  $\bf \begin{array}{ccllll} fred&irene\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 58&18\\ 57&17\\ 56&16\\ 55&15\\ ...&... \end{array}$

notice, Fred is always 40years older than Irene

thus, whatever age Irene is, let's say "i", then Fred is " i + 40 "

now, when is Fred 5 times Irene's age or 5*i or 5i? well, 

f = fred's age    i = irene's age

f = i + 40
now if  f = 5i

5i = i + 40   <---    solve for "i" to see how old Irene was then