Comparing percentage increases of tea and coffee

In a country the consumption of tea is five times that of coffee. If tea consumption is increased by $a\%$ and coffee by $b\%$, the total consumption rises by $7c\%$. If instead tea is increased by $b\%$ and coffee by $a\%$, the total consumption rises by $3c\%$. Find the relation between $a$ and $b$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. II. Proportion, Examples II, No. 24