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Sagot :
a = amount invested at 4%.
b = amount invested at 7%.
we know that whatever "a" and "b" may be, they total 27000, so we can say that a + b = 27000, likewise we can say that b = 27000 - a.
how much will it be for 4% of "a"? well, that's just (4/100) * a, or 0.04a.
how much will it be for 7% of "b"? well, that's just (7/100) * a, or 0.07b.
we also know that the earned interest by those two interest amounts is 1440, so
[tex]\begin{cases} a + b = 27000\\ b = 27000 - a \end{cases}\hspace{5em}0.04a~~ + ~~0.07b~~ = ~~1440 \\\\\\ \stackrel{\textit{substituting "b"}}{0.04a~~ + ~~0.07(27000-a)~~ = ~~1440}\implies 0.04a+1890-0.07a=1440 \\\\\\ 1890-0.03a=1440\implies -0.03a=-450\implies a=\cfrac{-450}{-0.03} \\\\\\ 15000=\textit{\LARGE a}\hspace{15em}\stackrel{27000~~ - ~~15000}{\textit{\LARGE b}=12000}[/tex]
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