Question

the average, or mean, t, of three exam grades, r, s, and z, is given by the following formula. ( t = \frac{r + s + z}{3} ) (a) solve the formula for ( z ). (b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 83% and 85%: ( r = 83 ) and ( s = 85 ). what must you get on the third exam to have an average of 90%? (a) the formula is ( z = square )

Explanation:

Part (a)

Step 1: Multiply both sides by 3

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

Step 2: Subtract \( r \) and \( s \) from both sides

To solve for \( z \), we need to isolate it. So we subtract \( r \) and \( s \) from both sides of the equation \( 3T = r + s + z \). This results in \( z = 3T - r - s \).

Step 1: Identify the values

We know that \( T = 90 \) (the desired average), \( r = 83 \), and \( s = 85 \). We will use the formula for \( z \) from part (a), which is \( z = 3T - r - s \).

Step 2: Substitute the values into the formula

Substitute \( T = 90 \), \( r = 83 \), and \( s = 85 \) into the formula: \( z = 3(90) - 83 - 85 \).

Step 3: Calculate the result

First, calculate \( 3(90) = 270 \). Then, subtract 83 and 85 from 270: \( 270 - 83 - 85 = 187 - 85 = 102 \).

Answer:

\( 3T - r - s \)

Part (b)