For this problem, we need to get to a 50% ratio first, and go from there. To do this, we have to combine 70% and 10% and then take the average of those to see if it reaches 50%.
The way I found it was just to test every combination, and eventually I found a mixture of two parts 70% solution and one part 10% solution gave us 3 parts of a 50% solution. So now that we have our ratios, we can solve.
$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{15}}\right) = {\mathtt{5}}$$
So 5 liters of 10% solution was used.
$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{15}}\right) = {\mathtt{10}}$$
And 10 liters of 70% solution was used.
