Question

A number increases by 10%, and then decreases by 10%. Will the result be greater than, less than, or equal to the original number? Explain.

Let x
represent the number. A 10% increase is equal to x+

, or
. A 10% decrease of this new number is equal to
− 0.1(
)
, or
.


Question 2
Because the result is
x
, the result is
the original number.

Answer 1

The result will be less than the original number

Explanation:

Let a = original number

for 10% increase = (100% + 10%) × a

= 110% × a

= 1.1 × a

= 1.1a

for 10% decrease of the new number = (100% - 10%) × 1.1a

= 90% × 1.1a

= 0.9 × 1.1a

= 0.99a

the result will be less than the original number, because the number that is decreased (1.1a) is greater than the number that is increased (a), therefore the decrement is greater than the increment, resulting the result smaller than the original number.