The given equation is (1/2)a + (2/3) b = 50
and b = 30
Substituting the given value of b is above the equation we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]
Therefore, a = 60 and b = 30 is a solution of the given equation.
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