Question

the average, or mean, t, of three exam grades, w, y, and x, is given by the following formula. ( t = \frac{w + y + x}{3} ) (a) solve the formula for x. (b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 83% and 88%: ( w = 83 ) and ( y = 88 ). what must you get on the third exam to have an average of 89%? (a) the formula is ( x = square ).

Explanation:

Part (a)

Step 1: Start with the formula

We have the formula for the mean \( T=\frac{w + y + x}{3} \). To solve for \( x \), first multiply both sides by 3 to eliminate the denominator.
\( 3T=w + y + x \)

Step 2: Isolate \( x \)

Subtract \( w \) and \( y \) from both sides of the equation.
\( x = 3T - w - y \)

Step 1: Identify the values

We know that \( w = 83 \), \( y = 88 \), and \( T = 89 \). We will use the formula \( x=3T - w - y \) from part (a).

Step 2: Substitute the values

Substitute \( T = 89 \), \( w = 83 \), and \( y = 88 \) into the formula:
\( x=3\times89 - 83 - 88 \)

Step 3: Calculate the result

First, calculate \( 3\times89 = 267 \). Then, \( 267-83 - 88=267-(83 + 88)=267 - 171 = 96 \)

Answer:

\( 3T - w - y \)

Part (b)