解:设每次所用的甲种金属$x$kg,原来这块合金中含甲种金属的百分比是$y,$根据题意,得
$\begin{cases}10y + x=\dfrac{3}{3 + 2}(10 + x)\\10y + x + x=\dfrac{7}{3 + 7}(10 + x + x)\end{cases},$
对$10y + x=\dfrac{3}{5}(10 + x)$化简得:
$10y + x = 6+\dfrac{3}{5}x,$
$10y=6+\dfrac{3}{5}x - x,$
$10y = 6-\dfrac{2}{5}x,$
$y=\dfrac{6-\dfrac{2}{5}x}{10},$
将$y=\dfrac{6-\dfrac{2}{5}x}{10}$代入$10y + x + x=\dfrac{7}{10}(10 + x + x)$得:
$10\times\dfrac{6-\dfrac{2}{5}x}{10}+2x=\dfrac{7}{10}(10 + 2x),$
$6-\dfrac{2}{5}x + 2x = 7+\dfrac{7}{5}x,$
$6+\dfrac{8}{5}x = 7+\dfrac{7}{5}x,$
$\dfrac{8}{5}x-\dfrac{7}{5}x = 7 - 6,$
$\dfrac{1}{5}x = 1,$
$x = 5。$
答:每次所用的甲种金属有$5$kg。