3. Two fields are planted with roses and lavender. $65 \%$ of the area of the first field is roses, $45 \%$ of the area of the second field is roses, and $53 \%$ of the area of both fields together is roses. What percentage of the total area (of both fields together) is the area of the first field?
Solution. Let's denote with $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ the area of the first and second field, respectively. Then, from the condition of the problem, we get that

$$
65 \% S_{1}+45 \% S_{2}=53 \%\left(S_{1}+S_{2}\right)
$$

from which we obtain that

$$
45 \%\left(S_{1}+S_{2}\right)+20 \% S_{1}=53 \%\left(S_{1}+S_{2}\right)
$$

or

$$
20 \% S_{1}=8 \%\left(S_{1}+S_{2}\right), \text { or } S_{1}=\frac{8}{20}\left(S_{1}+S_{2}\right)=\frac{40}{100}\left(S_{1}+S_{2}\right)=40 \%\left(S_{1}+S_{2}\right)
$$

The last equality shows that the first field is $40 \%$ of the total area of the two fields combined.