1 unit of input energy → Gives rise to 0.35 units of usable energy (since 65% is wasted)
while1 unit of input energy → Gives rise to 0.85 units of usable energy (since 15% is wasted).
Notice that we can "Scale up" or "scale down" any such statement, for example:
2 units of input energy → Gives rise to 2·(0.35) units of usable energy,
3 units of input energy → Gives rise to 3·(0.35) units of usable energy, etc.
k units of input energy → Gives rise to k·(0.35) units of usable energy, etc.
If we let k = 1/(0.35) then we can find out how much input-energy it takes to generate one unite of usable energy, under each system:
Similarly:
It may be clear already that we need to take a quotient of these
two numbers, but to make sure we understand what we're doing and to
avoid mistakes, let's simplify the fractions with our calculator and
write these more clearly as:
Similarly:
Plausibility check: It does indeed make sense that under the old (less efficient system, it takes more input-energy (about 2.857 units) to create one unit of usable energy, than under the new, more efficient system (which requires only about 1.1765 units of input energy) ☑
Finally, If we used to need A and now need B, we take which quotient? We look at B/A (for example if we used to need 4 and now need 3 unit, we would look at 3/4 and get 0.75% telling us we're using 0.75% of the input-energy we used to need, to generate the same). Thus we calculate:
1.1765/2.857 which equals 0.41179559...
To be more exact we should use the exact numbers to get: (1/(0.85)) / (1/(0.35)) which simplifies to (0.35)/(0.85) which per calculator equals 0.411764706.... which is ≈0.412 or ≈0.41
These would reflect using (under the new system) 41.2% of the energy we used to use (or more roughly, 41% of the energy we used to need) under the old energy system.
These represent a reduction by 58.8% or to the nearest percent, a reduction by 59%. This is significantly higher than the "50%" figure the mayor had stated, and which the newspaper quoted without checking!