Why does adding 10% and 5% of the same number together yield a different result that adding 15% of that number?

Question

This is a markup question. I am trying to add 10% overhead and 5% profit to a construction job and get different results and can not understand why?

Answer 1

The 15% increase adds 15% of the starting number.

X * 1.15 = 1.15X

 

The 10% increases the number  to 110%.

The additional 5% increase add 5% of what is now 110% of the original number.

X * 1.10 = 1.10X

1.10X * 1.05X = 1.15X

 

Something similar occurs when stores advertise 25% off, and another 10% at checkout.

The second discount is 10% of a reduced price, so it isn't really a 10% discount on the original sales price.