fat loss and muscle building

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Is it a reasonable goal to maintain muscle mass while focusing on losing fat? What about losing fat AND gaining muscle mass? I ask because the consensus seems to be that I will put on fat as I build muscle mass and I will lose muscle mass if I focus on losing fat.

I lift weights approximately five times per week I usually do roughly 10-15 minutes on an elliptical after the weights. This occurrs usually at 5:00 to 6:00 pm, which can't change. I go to bed around 9:00 to 9:45 and get up at 4:30, which can not change. Recently, I've changed from ignoring my legs while isolating all my individual upper body muscle groups and working them heavily on alternating days to switching between doing a few sets all the upper body muscles on one day, while working all of my leg muscles heavily on the next day. My heart rate has always been around 130 to 160 during the weights and can spike to max if I push it hard enough on the elliptical, which I don't do routinely.

I consume at at least 80-90 grams of protein post workout, which usually come from a protein shake mix and dinner. I usually skip breakfast or eat a breakfast bar with my commute coffee. I've been trying to eat a healthy lunch every day but have been skipping lately. I'm usually very successful with keeping hydrated 24/7.