Question

What single decimal multiplier would you use to decrease by 16% followed by a 14% increase?

Answer 1

Answer:

         0.9576

Step-by-step explanation:

Suppose you start with a quantity X.

Decreasing this by 16% means we are left with

       X - (16% of X)

   =  X - 0.16X

   =  0.84X

Now increasing this by 14% means we finish with

       0.84X  +  (14% of 0.84X)

   =  0.84X  +  0.14 × 0.84X

   =  (1 + 0.14) × 0.84X

   =  (1.14 × 0.84) × X

   =  0.9576 X

So a decrease of 16% followed by an increase of 14% is the same as multiplying by 0.9576  (which is a decrease of 4.24%).