Question

Joanna's pay for working overtime varies jointly as the number of hours she works and her hourly pay rate. If her overtime pay is $103.44 when she works 8 hours at an hourly rate of $8.62, then find the number of hours worked when her overtime pay is $213.75 at an hourly rate of $9.50.

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\\ variation \end{array}\\\\ -------------------------------\\\\`


`\bf \begin{cases} o=\textit{overtime pay}\\ h=\textit{hours worked}\\ p=\textit{payrate} \end{cases}\qquad \qquad o=\underline{k}hp \\\\\\ \textit{we know that } \begin{cases} o=103.44\\ h=8\\ p=8.62 \end{cases}103.44=k8\cdot 8.62\implies \cfrac{103.44}{8\cdot 8.62}=k \\\\\\ 1.5=k\implies \boxed{\cfrac{3}{2}=k}\qquad \qquad o=\cfrac{3}{2}hp`

now, what's "h" when the overtime pay is 213.75 and the payrate is 9.5?

well
`\bf \begin{cases} o=213.75\\ p=9.5 \end{cases}\implies 213.75=\cfrac{3}{2}\cdot h\cdot 9.5`

solve for "h"