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]
