The average, or mean, D, of three exam grades, $v, r$, and $w$, is given by the following formula. \[ D=\frac{v+r+w}{3} \] (a) Solve the formula for $w$. (b) Use the formula in part (a) to solve this problem. On your first two exams, your grades are $83 \%$ and $89 \%$ : $v=83$ and $r=89$. What must you get on the third exam to have an average of $89 \%$ ? (a) The formula is $w=3 D-r-v$. (b) The answer is $\%$.

Step 1 ：Given the formula for the average, or mean, D, of three exam grades, $v, r$, and $w$, is \(D=\frac{v+r+w}{3}\)

Step 2 ：Part (a) asks us to solve the formula for $w$. To do this, we need to isolate $w$ on one side of the equation. We can do this by subtracting $v$ and $r$ from both sides and then multiplying by 3. This gives us the formula \(w=3D-v-r\)

Step 3 ：Part (b) asks us to use the formula from part (a) to solve a specific problem. We are given that on the first two exams, the grades are $83 \%$ and $89 \%$ : $v=83$ and $r=89$. We are asked to find what grade must be achieved on the third exam to have an average of $89 \%$, so $D=89$

Step 4 ：Substituting the given values of $v$, $r$, and $D$ into the rearranged formula from part (a), we get \(w=3*89-83-89\)

Step 5 ：Solving the above equation, we find that \(w=95\)

Step 6 ：So, the final answer is: You must get a grade of \(\boxed{95 \%}\) on the third exam to have an average of $89 \%$