Question

the annual interest on 17,000 investment exceeds the interest on an 11,000 investment by 308 . the 17,000is invested at a 0.4% higher rate of interest than the 11,000 what is the interest rate of eacg investment

Answer 1

keeping in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

x =  percent rate for the 17000 investment.

y = percent rate for the 11000 investment.

so the amount for the 17000 interest will just be (x/100) * 17000, or namely 170x.

and the amount of interest earned for the 11000 is (y/100) * 11000, or just 110y.

now, regardless of what "x" and "y" are, we know that the interest from the 17000 is higher by 308 bucks, therefore 170x = 110y + 308.

we also know that the rate of x is higher as well than y by 0.4%, so then x = y + 0.4.

$\bf \begin{cases} 170x=110y+308\\ \boxed{x}= y +0.4\\[-0.5em] \hrulefill\\ 170\left( \boxed{y+0.4} \right)=110y+308 \end{cases} \\\\\\ 170y+68=110y+308\implies 60y=240\implies y=\cfrac{240}{60}\implies \blacktriangleright y=\stackrel{\%}{4} \blacktriangleleft \\\\\\ x=y+0.4\implies \blacktriangleright x=\stackrel{\%}{4.4} \blacktriangleleft$