3. If fresh grapes contain $75 \%$ water, and dried grapes contain $5 \%$ water, how many kilograms of fresh grapes are needed to obtain $130 \mathrm{~kg}$ of dried grapes?
Solution. Let $x$ denote the amount of fresh grapes needed to obtain $130 \mathrm{~kg}$ of dried grapes. In $130 \mathrm{~kg}$ of dried grapes, there is $95 \%$ dry matter, which means that in $130 \mathrm{~kg}$ of dried grapes, there is $\frac{95 \cdot 130}{100}=123.5 \mathrm{~kg}$ of dry matter. Since fresh grapes contain $75 \%$ water, they contain $25 \%$ dry matter. However, the dry matter does not change in mass during drying, so in $x$ kilograms of fresh grapes, there must be $123.5 \mathrm{~kg}$ of dry matter. Finally, from

$$
\frac{25 x}{100}=123.5
$$

we get that $x=494 \mathrm{~kg}$.