There are rather "simple explanations" -
Like saying "air density blah-blah" and be technical to impress everyone -
I am not that smart as an airline instructor -
I liked to use actual examples in classrooms, then go to the simulator and demonstrate -

Long ago, I used the basics of flying a jet airliner for newly hired pilots on the 727 -

You know from the basics that thrust has to counteract (be equal) to drag -
A good example for the 727 is the drag at 250 Knots IAS -
The 3 engines will produce thrust which with a fuel flow of 2,500 lbs/thrust per engine -

Fuel flow is directly proportional to thrust -

If you reduce your IAS to 200 knots, you need to reduce thrust per engine to about 2,000 lbs -
If you want to increase IAS to 300 knots. you need to increase thrust to about 3,000 lbs -

If you shut down an engine, the total thrust needed to remain at same speed will be the same -
If you are at speed of 250 knots, but only operate 2 engines (1 failed) you need 7,500 lbs fuel flow -
Remember that 250 knots requires 3 times 2,500 lbs fuel flow = 7,500 lbs fuel flow total -

Now, what do you get with your altitude and decrease in drag...?
At sea level, with 250 knots IAS, you get about 250 knots TRUE airspeed with 7,500 lbs fuel flow -
At 10,000 feet, 250 knots IAS, becomes 285 knots TRUE airspeed, with same 7,500 lbs fuel flow -
At 39,000 feet, 250 knots IAS becomes 465 knots TRUE with same 7,500 lbs fuel flow -

Do you now see why you save fuel (and fly faster) when HIGHER with the amount of fuel you burn...?
These are all 727 figures - I use the Jeppesen CR-3 flight computer slide rule -