$$Costof3applesand4oranges=\mathrm{\$}3.47$$

$$Costof12oranges=\mathrm{\$}6.36$$

$$Totalamount=\mathrm{\$}10$$

$$Costof1orange=\frac{6.36}{12}=\mathrm{\$}0.53$$

$$Costof4orange=4\times 0.53=\mathrm{\$}2.12$$

$$Costof3apples=\mathrm{\$}3.47-\mathrm{\$}2.12=\mathrm{\$}1.35$$

$$Costof1apples=\frac{1.35}{3}=\mathrm{\$}0.45$$

So the number of apples she can buy today is

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