namely the interest yield is $870, so all those investments yielded that much after a year.
a = the whole amount he invested.
let's keep in mind that whatever% of anything is just (whatever/100) * anything.
now 1/5 of "a" went with 4%, how much is 1/5 of "a"? well is (1/5)a or a/5.
how much is 4% of a/5? well is just (4/100) * (a/5) or 0.04a/5.
he invested 1/2 at 5%, namely (1/2)a or a/2, and 5% of that is just (5/100) (a/2) or 0.5a/2.
and the rest, hmmm what's the rest? well, 1/2 taken up and then 1/5 taken up, so the rest is the difference of the full amount minus those hmmm let's see
[tex]\bf a-\cfrac{a}{5}-\cfrac{a}{2}\implies \cfrac{10a-2a-5a}{10}\implies \cfrac{3a}{10}[/tex]
and that was invested at 3.5%, what is 3.5% of that? well is just (3.5/100) * (3a/10), or 0.105a/10.
we know the sum of all those yields was 870 bucks, thus
[tex]\bf \cfrac{0.04a}{5}~~+~~\cfrac{0.05a}{2}~~+~~\cfrac{0.105a}{10}~~=~~870\impliedby
\begin{array}{llll}
\textit{let's multiply both}\\
\textit{sides by }\stackrel{LCD}{10}~to\\
\textit{toss the denominators}
\end{array}
\\\\\\
2(0.04a)+5(0.05a)+0.105a=8700
\\\\\\
0.08a+0.25a+0.105a=8700\implies 0.435a=8700
\\\\\\
a=\cfrac{8700}{0.435}\implies a=20000[/tex]
