Question

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?

Answer 1

month 6

Explanation:

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Answer 2

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