# Question 25a29

Oct 27, 2016

Jake is $\frac{48}{49}$ years old; Jan is $1 \frac{47}{49}$ years old.
Unlikely that this was the intended answer but I couldn't find any way of interpreting the question that gave reasonable results.

#### Explanation:

(Assuming "5 2a times Jake's.." should be "52 times Jake's..."
and that the "less 48" applies to 52 times Jake's age).

Let Jake's age be $x$
and Jan's age be $y$

We are told
[1]$\textcolor{w h i t e}{\text{XXX}} y = 2 x$
and
[2]$\textcolor{w h i t e}{\text{XXX}} x + y = 52 x - 48$

Substituting $2 x$ for $y$ (from [1]) into [2]
color(white)("XXX")x+2x=52x-48

#color(white)("XXX")3x=52x-48

$\textcolor{w h i t e}{\text{XXX}} 0 = 49 x - 48$

$\textcolor{w h i t e}{\text{XXX}} 48 = 49 x$

$\textcolor{w h i t e}{\text{XXX}} x = \frac{48}{49}$

and since $y = 2 x$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = 1 \frac{47}{49}$