$4,845 is invested, part at 13% and the rest at 7%. if the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 7% by $188.65, how much is invested at each rate?

a = amount invested at 13%

b = amount invested at 7%

how much is 13% of a ? well is (13/100) * a or 0.13a.

how much is 7% of b ? well is (7/100) * b or 0.07b.

we know the interest earned by a is whatever b is plus 188.65, since it exceeds it by that much, so 0.13a = 0.07b + 188.65.

we also know that both amounts must add up to 4845, thus a + b = 4845.

so, what is b anyway? well b = 4845 - a.

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