1 kg carrot = 50 gr carrot
To save weight for your hike, one way is bring dry food. This is really easy to do yourself and I would say also much tastier. Today I dried 1 kilo carrots and now it has a weight of 50 gr.
I sliced the carrots really thin and small. Pre-cook them for a little while, just so they get a little soft but still with a little crunch left. Rinse them in cold water and but them on a baking-plate to dry in the oven. Set the oven to less than 50° C and leave the door open to let the moist get out.