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%?

Answer 1

(a/2)(3b/2)=3ab/4 whereas ab=ab so we can now use the percent change formuala...

100(3ab/4-ab)/ab

100((3ab-4ab)/4)/ab

100(-ab)/(4ab)

-100/4

-25%

So the product will be *decreased* by 25%.

Answer 2

(a/2)(3b/2)=3ab/4 whereas ab=ab so we can now use the percent change formuala...

100(3ab/4-ab)/ab

100((3ab-4ab)/4)/ab

100(-ab)/(4ab)

-100/4

-25%

So the product will be reduced by 25%.