Question

Will the product of two numbers increase or decrease and by what percent if one of them is increased by 50%, and the other is decreased by 50%?
PLZ HELP! Need this quick! Thx! :D

Answer 1

:D

Let x be our first number and y be our second number.

The product of the two numbers will be xy.

Now let x be the one that increases by 50% and y be the one that decreases by 50%.

We can represent that by 1.5x and 0.5y, respectively.  If you are confused by that, let me explain.  If something increases by 50%, it becomes 1.5 times larger. So for x, that means 1.5x.
And if something decreases by 50%, it becomes 0.5 times smaller.  So for y, that means 0.5y.

Therefore we have 1.5x and 0.5y.  And the product of those two:

(1.5x) * (0.5y) = (3/2)x * (1/2)y = (3/4)xy

So our product is now (3/4)xy.

Comparing this answer to our original product of xy, we see that it is now only 3/4 as much or 75% of what it originally was.

Therefore, the product will DECREASE by 25%.

*DROPS MIC