Question

the average, or mean, d, of three exam grades, z, v, and s, is given by the following formula. ( d = \frac{z + v + s}{3} ) (a) solve the formula for s. (b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 83% and 85%: ( z = 83 ) and ( v = 85 ). what must you get on the third exam to have an average of 89%? (a) the formula is ( s = square ).

Explanation:

Part (a)

Step1: Multiply both sides by 3

To isolate the numerator, we multiply both sides of the equation \( D = \frac{z + v + s}{3} \) by 3. This gives us \( 3D = z + v + s \).

Step2: Subtract z and v

Now, we want to solve for \( s \), so we subtract \( z \) and \( v \) from both sides of the equation \( 3D = z + v + s \). This results in \( s = 3D - z - v \).

Step1: Identify given values

We know that \( z = 83 \), \( v = 85 \), and \( D = 89 \). We will use the formula from part (a), \( s = 3D - z - v \).

Step2: Substitute values into formula

Substitute \( z = 83 \), \( v = 85 \), and \( D = 89 \) into the formula: \( s = 3\times89 - 83 - 85 \).

Step3: Calculate the result

First, calculate \( 3\times89 = 267 \). Then, subtract 83 and 85 from 267: \( 267 - 83 - 85 = 184 - 85 = 99 \).

Answer:

\( 3D - z - v \)

Part (b)