4. A student's income comes from three sources: scholarship, temporary part-time work, and parental support. If the government doubles the scholarship, the income will increase by $5 \%$. If the time spent on part-time work is doubled, the income will increase by $15 \%$. By what percentage will the student's income increase if his father and mother send twice as much money?
Solution. Let $\mathrm{S}$ be the student's monthly income, $a, b$ and $c$ be the amounts of the scholarship, part-time job, and parental support, respectively (expressed, for example, in rubles). Clearly, $S=a+b+c$. Then, according to the conditions, $2 a+b+c=1.05 S$ and $a+2 b+c=1.15 S$. From the first equation, $a=0.05 S$, and from the second, $b=0.15 S$, then $c=S-a-b=0.8 S, a+b+2 c=1.8 S$, which means the student's income will increase by $80 \%$. Answer: $80 \%$.