$$ Cost\ of\ 3\ apples\ and\ 4\ oranges=\$ 3.47 $$

$$ Cost\ of\ 12\ oranges=\$ 6.36 $$

$$ Total\ amount=\$10 $$

$$ Cost\ of\ 1\ orange=\frac{6.36}{12}=\$0.53 $$

$$ Cost\ of\ 4\ orange=4\times 0.53=\$2.12 $$

$$ Cost\ of\ 3\ apples=\$3.47-\$2.12=\$1.35 $$

$$ Cost\ of\ 1\ apples=\frac{1.35}{3}=\$0.45 $$

So the number of apples she can buy today is

$$ Apples=\frac{10}{0.45}=22.22\approx 22 $$