Question

the average, or mean, t, of three exam grades, s, y, and z, is given by the following formula.
t = \frac{s + y + 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 84% and 89%. s = 84 and y = 89. what must you get on the third exam to have an average of 90%?
(a) the formula is z = \square.

Explanation:

Part (a)

Step1: Multiply both sides by 3

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

Step2: Subtract s and y from both sides

To solve for \( z \), we subtract \( s \) and \( y \) from both sides of the equation \( 3T = s + y + z \). So, \( z = 3T - s - y \).

Step1: Identify the values

We know that \( T = 90 \), \( s = 84 \), and \( y = 89 \). We will use the formula \( z = 3T - s - y \) from part (a).

Step2: Substitute the values

Substitute \( T = 90 \), \( s = 84 \), and \( y = 89 \) into the formula: \( z = 3\times90 - 84 - 89 \).

Step3: Calculate the result

First, calculate \( 3\times90 = 270 \). Then, \( 270 - 84 = 186 \), and \( 186 - 89 = 97 \).

Answer:

\( 3T - s - y \)

Part (b)