Question

which shows the correct solution of the equation \\(\frac{1}{2}a + \frac{2}{3}b = 50\\), when \\(b = 30\\)? \\(\frac{1}{2}a + \frac{2}{3}(30) = 50\\)

Explanation:

Step1: Substitute \( b = 30 \)

Substitute \( b = 30 \) into the equation \( \frac{1}{2}a+\frac{2}{3}b = 50 \), we get \( \frac{1}{2}a+\frac{2}{3}(30)=50 \).

Step2: Simplify the term with \( b \)

Calculate \( \frac{2}{3}(30) \), \( \frac{2}{3}\times30 = 20 \), so the equation becomes \( \frac{1}{2}a + 20 = 50 \).

Step3: Solve for \( a \)

Subtract 20 from both sides: \( \frac{1}{2}a = 50 - 20 = 30 \). Then multiply both sides by 2: \( a = 30\times2 = 60 \).

Answer:

The solution is \( a = 60 \) (after following the steps of substituting \( b = 30 \), simplifying, and solving for \( a \)).