An 80% decrease followed by a 100% increase is the same as a 50% decrease followed by what other percent decrease?

Question

An 80% decrease followed by a 100% increase is the same as a 50% decrease followed by what other  percent decrease?

anonymous · Answer

I used simple numbers.

80% decrease$$100-80=20$$
100% increase$$20+20=40$$
50% decrease$$100-50=50$$
Other decrease$$50-10=40$$
Other decrease is 10%

anonymous · Answer

answer is 20%.Please can you try again

anonymous · Answer

$$x(1-0.8) + x(1+1) = x(1-0.5) + x(1-y)$$

anonymous · Answer

can you explain

anonymous · Answer

Rogenhamen's explanation is correct, however the last decrease should be 20%.

anonymous · Answer

Oh, 20% of 50 is 10.

anonymous · Answer

Let me explain my method. If we decrease 100 by 80%, this can be expressed as$$100 - 100*0.8$$If we factor 100 out, we get the following expression$$100(1-0.8)$$
I used this idea to express the percent increases and increases of the problem. Since the two must equal each other, we can set them equal to each other. 

We need to find the value of $y$ such that the equality is satisfied. You'll see that it will equal 0.2. 0.2*100 = 20%

anonymous · Answer

Thank you