Step-by-step explanation:
Given
[tex]q + p = 2(q - p)[/tex]
as equation 1.
I used q-p as the difference as logically the woman will be older than her son.
Also given,
[tex]qp = 675[/tex]
as equation 2.
Using equation 2,
[tex]q = \frac{675}{p} [/tex]
substitute this equation into equation 1.
[tex] \frac{675}{p} + p = 2( \frac{675}{p} - p) \\ \frac{675}{p} + p = \frac{1350}{p} - 2p \\ \frac{675}{p} - \frac{1350}{p} = - 2p - p \\ - 3p = - \frac{675}{p} \\ - 3p \times p = - 675 \\ - 3 {p}^{2} = - 675 \\ {p}^{2} = - 675 \div - 3 \\ {p}^{2} = 225 \\ p = \sqrt{225} \\ = 15[/tex]
Substitute P into equation 2.
[tex]15q = 675 \\ q = 675 \div 15 \\ = 45[/tex]
Therefore the woman is 45 years old while her son is 15 years old.
