Question

The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $25 item is $25.75, what is the total cost on a $60 item?


a)$60.75


b)$618


c)$61.80


d)$103

Answer 1

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

$\bf \stackrel{\textit{\underline{c} varies directly proportional to \underline{p}}}{c=kp} \\\\\\ \textit{we also know that } \begin{cases} p=25\\ c=25.75 \end{cases}\implies 25.75=k25\implies \cfrac{25.75}{25}=k \\\\\\ 1.03=k~\hspace{10em}\boxed{c=1.03p} \\\\\\ \textit{when p = 60, what is \underline{c}?}\qquad c=1.03(60)\implies c=61.8$

Answer 2

60.75 is the answer