Question

A library expansion begun in 2002 was expected to cost 107million. By 2006 library officials estimate the cost would be 31million over budget. By what percent did the actual cost exceed the initial estimate?

Answer 1

The best way to solve this problem is by doing a cross multiplication set up. 

$\frac{107}{138}* \frac{100%}{?}$
remember numbers on one side percents on the other. 
what we know:
107= the number originally thought to be the cost of expansion
138= the new estimated cost of expansion (107+31)
100%= is equal to 107 because this was our original starting number

alright now we find "?" 

138*100=13800
13800÷107= 128.97  or 129%

this means that the expansion was 29% over budget<span />