The given information and the equation $\displaystyle{y}={k}{x}\usepackage{cmbright}\Huge\$ give you $\displaystyle{84}={k}{\left({12}\right)}\usepackage{cmbright}\Huge\$ . Solve to find $\displaystyle{k}={7}\usepackage{cmbright}\Huge\$ . Now substitute this and $\displaystyle{y}={140}\usepackage{cmbright}\Huge\$ into $\displaystyle{y}={k}{x}\usepackage{cmbright}\Huge\$ :

$\displaystyle{140}={7}{x}\usepackage{cmbright}\Huge\$

$\displaystyle{x}={20}\usepackage{cmbright}\Huge\$

Joan will need to work 20 hours.