Question

the interest earned on an account varies directly with the balance in the account. if an account with a balance of $200 earns $12.5 in interest, find the amount of interest earned on an account with a balance of 500

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{\underline{I}nterest varies with \underline{b}alance}}{I=kb}\qquad \qquad \textit{we know that } \begin{cases} b=200\\ I=12.5 \end{cases} \\\\\\ 12.5=k200 \implies \cfrac{12.5}{200}=k\implies \cfrac{~~\frac{125}{10}~~}{\frac{200}{1}}=k\implies \cfrac{125}{10}\cdot \cfrac{1}{200}=k \\\\\\ \cfrac{1}{16}=k \qquad \qquad \textit{therefore}\qquad \boxed{I=\cfrac{1}{16}b} \\\\\\ \textit{when b = 500, what is \underline{I}?}\qquad I=\cfrac{1}{16}(500)\implies I=\cfrac{125}{4}\implies I=31.25$