I find it both good to know and very likely that tasks like this will be tested in the ccie lab. So I did some extra training to become more comfortable with this kind of tasks with EIGRP. The task in my example is just taken out of nowhere, but Im going to solve it with a general approach.
Make sure that traffic to the network depicted as a switch is loadbalanced from Router E between both paths, and Path A should be used 6 times as much as the other! The routers are configured with metric weights 0 0 1 0 0, in other words, only k3=1, so delay would be the only parameter for metric calculations.