Question

Which amount is larger and by how much? A positive number a or the same number a increased by 50% and then decreased by 50% of the result?

Answer 1

The original positive number a is larger than the same number increased by 50% and then decreased by 50%. This is because the latter operation effectively decreases the original number by 25%.

Step-by-step explanation:

The student asked which amount is larger and by how much: a positive number a, or the same number a increased by 50% and then decreased by 50% of the result. Let's calculate both scenarios:

Increasing a by 50% gives us a + (0.5 × a) = 1.5a.

Then, decreasing this result by 50% gives (1.5a) - (0.5 × 1.5a) = 0.75a.

Comparing the original number a with 0.75a, it's clear that a is larger because 0.75a is equal to a reduced by 25%.

Therefore, the original number a is larger than the result of increasing by 50% followed by a decrease of 50%, and it is larger by 25% of a.

Answer 2

The original positive number will be more.

Step-by-step explanation:

In order to find this, we can first call the original positive number a. Now to find how much it would be when we add 50% of that, we can create the following equation.

a + .5a = 1.5a

Now we need to take 50% of that result. To do that, we can multiply by .5.

1.5a * .5 = .75a

Since the end result of the adding and subtracting 50% is .75a, we know that it is less than the original number.