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Robin Clark 2010-08-15 11:02:25 +01:00
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\documentclass[a4paper,10pt]{article}
\title{A mother is 21 years older than the child. 6 years from now the mother will be 5 times as old as the child.
Question: Where is the father ? }
\author{A. Puzzle}
\begin{document}
\maketitle
\begin{abstract}
Spoiler alert ! Do not read if you want to work it out yourself.
\end{abstract}
answer overleaf...
\clearpage
\paragraph{The answer....}
Mother is 21 years older than child so, using $m$ for the age of the mother and $c$
for the age of the child.
$$ c + 21 = m $$
\begin{equation}
\label{s1}
c = m - 21
\end{equation}
In 6 years time the mother is 5 times older than the child SO...
$$ 5(c+6) = m + 6 $$
So
$$ 5c + 30 = m + 6 $$
\begin{equation}
\label{s2}
5c = m - 24
\end{equation}
Subtracting Equation (\ref{s1}) {\em from} Equation (\ref{s2}) gives:
$$ 5c - c = m - m -24 - (-21) $$
$$ 4c = -3 $$
$$ c = -3/4 $$
The baby is therefore -0.75 years old at present.
which is -9 months. So the Baby is being conceived, so we know where the father is afterall!
\end{document}