Diophantus Updated/Solution

Solution to Diophantus Updated

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Amanda is $21$ years older than her son John.

In $6$ years from now, Amanda will be $5$ times as old as John.

Inside Amanda.

Let $M$ be the age in years of Amanda now.

Let $C$ be the age in years of John now.

We have:

$\ds M$

$=$

$\ds C + 21$

Amanda is $21$ years older than her son John.

$\ds M + 6$

$=$

$\ds 5 \paren {C + 6}$

In $6$ years from now, Amanda will be $5$ times as old as John.

$\ds \leadsto \ \ $

$\ds C + 21 + 6$

$=$

$\ds 5 \paren {C + 6}$

substituting for $M$

$\ds \leadsto \ \ $

$\ds C + 27$

$=$

$\ds 5 C + 30$

simplifying

$\ds \leadsto \ \ $

$\ds -3$

$=$

$\ds 4 C$

subtracting $C + 30$ from both sides

$\ds \leadsto \ \ $

$\ds C$

$=$

$\ds -\frac 3 4$

So John is $-\dfrac 3 4$ years old, that is, $-9$ months.

That is, John will be born in $9$ months time.

So, right now, John's father is inside Amanda.

$\blacksquare$