Answer :

Of course, let's solve the equation step by step.

Given the equation:
[tex]\[ \frac{1}{2} a + \frac{2}{3} b = 50 \][/tex]
and knowing that \( b = 30 \), we can substitute \( b \) into the equation.

Step 1: Substitute \( b \) into the equation
[tex]\[ \frac{1}{2} a + \frac{2}{3} (30) = 50 \][/tex]

Step 2: Simplify the term involving \( b \)
Calculate \( \frac{2}{3} \times 30 \):
[tex]\[ \frac{2}{3} \times 30 = 20 \][/tex]

So the equation now looks like:
[tex]\[ \frac{1}{2} a + 20 = 50 \][/tex]

Step 3: Isolate the term with \( a \)
Subtract 20 from both sides of the equation:
[tex]\[ \frac{1}{2} a = 50 - 20 \][/tex]
[tex]\[ \frac{1}{2} a = 30 \][/tex]

Step 4: Solve for \( a \)
Multiply both sides by 2 to isolate \( a \):
[tex]\[ a = 30 \times 2 \][/tex]
[tex]\[ a = 60 \][/tex]

So the solution to the equation \( \frac{1}{2} a + \frac{2}{3} b = 50 \) when \( b = 30 \) is:
[tex]\[ a = 60 \][/tex]