Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The
same principal invested in the other CD earns $360. Find the two rates of interest. Smaller value and Larger value (%)
1 answer:
a = interest rate of first CD
b = interest rate of second CD
and again, let's say the principal invested in each is $X.
![\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\](https://tex.z-dn.net/?f=%5Cbf%20a-b%3D3%5Cqquad%20%5Cimplies%20%5Cqquad%20%5Cboxed%7Bb%7D%3D3%2Ba~%5Chfill%20%5Cbegin%7Bcases%7D%20%5Cleft%28%20%5Cfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5C%5C%5C%5C%20%5Cleft%28%20%5Cfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Ba%7D%7B100%7D%20%5Cright%29X%3D240%5Cimplies%20X%3D%5Ccfrac%7B240%7D%7B~~%5Cfrac%7Ba%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B24000%7D%7Ba%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%20%5Ccfrac%7Bb%7D%7B100%7D%20%5Cright%29X%3D360%5Cimplies%20X%3D%5Ccfrac%7B360%7D%7B~~%5Cfrac%7Bb%7D%7B100%7D~~%7D%5Cimplies%20X%3D%5Ccfrac%7B36000%7D%7Bb%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C)


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