35 lines
1.0 KiB
TeX
35 lines
1.0 KiB
TeX
\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}
|