Just Curious

My co-worker and I needed to solve an equation for a spreadsheet at work, neither of us is terribly math inclined. We both came up with different equations that lead to the correct answer and we started with the same data set. We were curious to know why the two numbers ended up the same even though we both took different paths to the same result? Its amazing how two people can solve a problem two different ways and get to the correct answer. Thanks for your time! :)

Equation 1: 18383.38 - (18383.38 * .0675) = 17142.5

Equation 2: 18383.38 / (1 + (6.75 / (100 - 6.75))) = 17142.5

Equation 1 has a common factor of 18383.38

18383.38 - (18383.38 * .0675) = 18383.38*(1 - 0.0675) = 18383.38*0.9325

2nd equation:

18383.38 / (1 + (6.75 / (100 - 6.75))) = 18383.38/(1+(6.75/93.25))

6.75/93.25 simplifies to 27/373

=18383.38/(1+(27/373)) = 18383.38/(400/373) = 18383.38*(373/400)

And 373/400 = 0.9325 (Wink)

OMG that makes sense! Thank you so much, math is fun!