So.. le'ts say he invested "a" amount at 7%.
now, how much is 7% of a? well, (7/100) * a, or
0.07a.
then he invested some more at 12%
in fact "<span>$3000 more than twice the amount" of "a" is what he invested at 12%.
now, what's twice the amount of "a"? well, 2a.
what's 3000 more than that? well,
2a + 3000so, he invested that much at 12%, how much is 12% of 2a+3000? well, (12/100) * (2a + 3000), or just 0.12(2a+3000)
we also know that, the interest earned from both investments is 4700, thus
0.07a + 0.12(2a+3000) = 4700
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![\bf \stackrel{\textit{at 7\%}}{0.07a}+\stackrel{\textit{at 12\%}}{0.12(2a+3000)}=4700\implies 0.07a+0.24a+360=4700 \\\\\\ 0.31a=4700-360\implies 0.31a=4340\implies a=\cfrac{4340}{0.31} \\\\\\ \boxed{a=14000}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bat%207%5C%25%7D%7D%7B0.07a%7D%2B%5Cstackrel%7B%5Ctextit%7Bat%2012%5C%25%7D%7D%7B0.12%282a%2B3000%29%7D%3D4700%5Cimplies%200.07a%2B0.24a%2B360%3D4700%0A%5C%5C%5C%5C%5C%5C%0A0.31a%3D4700-360%5Cimplies%200.31a%3D4340%5Cimplies%20a%3D%5Ccfrac%7B4340%7D%7B0.31%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Ba%3D14000%7D)
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how much was invested at 12%? well, 2a + 3000.</span>