解:
(1)设足球的单价是$x$元,跳绳的单价是$y$元,
根据题意,得$\begin{cases}30x + 60y = 720\\10x + 50y = 360\end{cases}$
由$10x + 50y = 360$得$x = 36 - 5y,$
将$x = 36 - 5y$代入$30x + 60y = 720$得:
$30(36 - 5y) + 60y = 720$
$1080 - 150y + 60y = 720$
$-90y = 720 - 1080$
$-90y = -360$
$y = 4$
把$y = 4$代入$x = 36 - 5y$得:
$x = 36 - 5×4 = 36 - 20 = 16$
答:足球的单价是16元,跳绳的单价是4元.
(2)设该店的商品按原价的$m$折销售,
根据题意,得$16×\frac{m}{10}×100 + 4×\frac{m}{10}×100 = 1800$
$160m + 40m = 1800$
$200m = 1800$
$m = 9$
答:该店的商品按原价的9折销售.