Question

the average, or mean, t, of three exam grades, z, w, and r, is given by the following formula.
( t = \frac{z + w + r}{3} )
(a) solve the formula for r.
(b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 86% and 85%: ( z = 86 ) and ( w = 85 ). what must you get on the third exam to have an average of 90%?

(a) the formula is ( r = square ).

Explanation:

Part (a)

Step1: Multiply both sides by 3

To isolate the numerator, multiply each side of the equation \( T = \frac{z + w + r}{3} \) by 3. This gives \( 3T = z + w + r \).

Step2: Subtract z and w

Subtract \( z \) and \( w \) from both sides to solve for \( r \). So, \( r = 3T - z - w \).

Step1: Identify values

We know \( T = 90 \), \( z = 86 \), and \( w = 85 \). Use the formula from part (a): \( r = 3T - z - w \).

Step2: Substitute values

Substitute the known values into the formula: \( r = 3(90) - 86 - 85 \).

Step3: Calculate

First, calculate \( 3(90) = 270 \). Then, \( 270 - 86 - 85 = 270 - 171 = 99 \).

Answer:

\( 3T - z - w \)

Part (b)