Question

This is a variation acitivity:


For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 year earns interest of $320, how much interest would be earned in if you deposit $5000 for 7 years?


To set it up so far for step 1, I have S = KPT


S = Simple interest

P = Principal

T = Time


I know I have to solve for K first using the information then fill in K to get the second half for the answer. I just don’t know how to do that with this question considering the wording.

Answer 1

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

$\bf \stackrel{\textit{\underline{I} varies jointly with \underline{P} and \underline{t}}}{I=kPt} \\\\\\ \textit{we also know that } \begin{cases} P=2000\\ t=4\\ I=320 \end{cases}\implies 320=k(2000)(4)\implies \cfrac{320}{(2000)(4)} \\\\\\ 0.04=k\qquad therefore\qquad \boxed{I=0.04Pt} \\\\\\ \textit{if P=5000 and t=7, what is \underline{I}?}\qquad I=0.04(5000)(7)\implies I=1400$