Question

the average, or mean, d, of three exam grades, r, y, and w, is given by the following formula.
d = \frac{r + y + 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 84% and 85%: r = 84 and y = 85. what must you get on the third exam to have an average of 88%?
(a) the formula is w = \square.

Explanation:

Part (a)

Step 1: Multiply both sides by 3

To eliminate the denominator in the formula \( D = \frac{r + y + w}{3} \), we multiply both sides of the equation by 3. This gives us \( 3D = r + y + w \).

Step 2: Subtract r and y from both sides

To solve for \( w \), we need to isolate it. We subtract \( r \) and \( y \) from both sides of the equation \( 3D = r + y + w \). This results in \( w = 3D - r - y \).

Step 1: Identify the values

We know that \( r = 84 \), \( y = 85 \), and \( D = 88 \). We will use the formula for \( w \) from part (a), which is \( w = 3D - r - y \).

Step 2: Substitute the values into the formula

Substitute \( r = 84 \), \( y = 85 \), and \( D = 88 \) into the formula: \( w = 3\times88 - 84 - 85 \).

Step 3: Calculate the value

First, calculate \( 3\times88 = 264 \). Then, subtract 84 and 85 from 264: \( 264 - 84 - 85 = 180 - 85 = 95 \).

Answer:

\( 3D - r - y \)

Part (b)