The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities. The Gades Foundation donated $250 in the first month, and each month afterward their cumulative donation total increases by $100. The HBM Corporation donated $64 in the first month, and each month afterward their cumulative donation total increases by 75 %. In which month will the HBM Corporation's cumulative donation total first exceed the Gades Foundations' cumulative donation total?

The HBM Corporation's cumulative donation total first exceed the Gades Foundations' cumulative donation total on the SIXTH (6TH) MONTH.

Gades Foundation     
                 donation       cumulative total
1st month   250                 250
2nd month 100                 350
3rd month  100                 450
4th month  100                  550
5th month  100                  650
6th month  100                  750

y = 250 + 100(n-1)
y = 250 + 100(6-1) = 250 + 500 = 750

HBM Corp.           
                     donation      cumulative total
1st month       64                        64                   
2nd month      48                      112            
3rd month       84                      196          
4th month     147                      343        
5th month     257                      600     
6th month     450                  1,050

y = 64 * (1.75)^(n-1)
y = 64 * (1.75) ⁽⁶⁻¹⁾ = 64 * (1.75)⁵ = 64 * 16.41 = 1,050