This would give you the correct cost for the first mixture, but not for the second. You probably made an addition error when combining the two equations to eliminate a variable. You should be starting with the two equations: $\displaystyle{12}{S}+{4}{C}={42}\usepackage{cmbright}\Huge\$ and $\displaystyle{4}{S}+{12}{C}={30}\usepackage{cmbright}\Huge\$ . Multiply the first equation by $\displaystyle-{3}\usepackage{cmbright}\Huge\$ and add this to the second equation.