Question

Suppose you add 10% of a number to the number, and then you subtract 10% of the total. Is the the result greater than, less than, or equal to the original number? Explain your reasoning.

Answer 1

It would be equal to because it would be like if you had 6 cards and someone gave you 2 more cards but then took away 2 cards you would end up with 6.

Answer 2

Less than

Explanation:

Let x be the number. We can write an expression with 10% of x added to x. We can convert 10% to 0.1:

`=10/100=0.1`

Therefore:

`=0.1\cdot{x}+x=1.1\cdot{x}`

If we subtract 10% of 1.1x from 1.1x:

`=1.1\cdot{x}-0.1\cdot{1.1\cdot{x}}=0.99\cdot{x}`

We get 0.99x which isless than the original number.