Question

Which amount is larger and by how much?

A positive number A or the same number A decreased by 50% and then increased by 50% of the result? Please help.

Answer 1

a*(1 -0.5)*(1 +0.5) = 0.75a . . . . the original number "a" is larger

(a/(0.75a) -1) * 100% = 33 1/3% . . . . the original number is larger by 33 1/3% of the revised number

Explanation:

Answer 2

• a is larger by 33.33%

Explanation:

Initial number = a

Decrease by 50%

• a - 50% =
• a - 0.5a =
• 0.5a

Increase by 50%

• 0.5a + 50% =
• 0.5a + 0.5*0.5a =
• 0.75a

The difference between the initial and final numbers:

• a - 0.75a = 0.25a

Percent difference:

• (0.25a/0.75a)*100% = 33.33%