1. **State the problem:** We are given two equations: $a + b = 67$ and $a^b = 76$. We need to find the value of $b + d$. 2. **Analyze the problem:** We have two variables $a$ and $b$ in the equations, but the expression to find includes $d$, which is not defined or related to $a$ or $b$ in the problem. 3. **Attempt to solve for $a$ and $b$:** From $a + b = 67$, we can express $a = 67 - b$. 4. Substitute into the second equation: $a^b = (67 - b)^b = 76$. 5. Since $76$ is a small number and $67 - b$ must be positive, try integer values for $b$ to satisfy $(67 - b)^b = 76$. 6. Check $b=1$: $(67 - 1)^1 = 66$ (not 76). 7. Check $b=2$: $(67 - 2)^2 = 65^2 = 4225$ (too large). 8. Check $b=3$: $(67 - 3)^3 = 64^3 = 262144$ (too large). 9. Check $b=0$: $(67 - 0)^0 = 67^0 = 1$ (not 76). 10. Check $b=4$: $(67 - 4)^4 = 63^4$ (very large). 11. Check $b=5$: $(67 - 5)^5 = 62^5$ (very large). 12. Since no integer $b$ satisfies the equation, and $d$ is undefined, the problem cannot be solved as stated. **Final answer:** Cannot determine $b + d$ because $d$ is undefined and no integer $b$ satisfies the given equations.