1. **State the problem:** Given $a=5$ and $b=3$, solve the equation $$ (2a)^2 = 3b $$ for the values of $a$ and $b$. 2. **Write the formula and substitute values:** The equation is $$ (2a)^2 = 3b $$ Substitute $a=5$ and $b=3$: $$ (2 \times 5)^2 = 3 \times 3 $$ 3. **Calculate each side:** Left side: $$ (10)^2 = 100 $$ Right side: $$ 9 $$ 4. **Compare both sides:** $$ 100 \neq 9 $$ 5. **Conclusion:** The equation $$ (2a)^2 = 3b $$ is not true for $a=5$ and $b=3$ because the left side equals 100 and the right side equals 9. If you want to find $b$ such that the equation holds for $a=5$, solve for $b$: $$ (2a)^2 = 3b \implies b = \frac{(2a)^2}{3} $$ Substitute $a=5$: $$ b = \frac{(2 \times 5)^2}{3} = \frac{100}{3} \approx 33.33 $$ So, for $a=5$, $b$ must be approximately 33.33 for the equation to hold.