Question

the average, or mean, t, of three exam grades, r, w, and y, is given by the following formula. ( t = \frac{r + w + y}{3} ) (a) solve the formula for ( y ). (b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 84% and 89%: ( r = 84 ) and ( w = 89 ). what must you get on the third exam to have an average of 87%? (a) the formula is ( y = square ).

Explanation:

Part (a)

Step1: Start with the formula

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

Step2: Isolate y

Subtract \( r \) and \( w \) from both sides of the equation to solve for \( y \).
\( y = 3T-r - w \)

Step1: Identify the values

We know that \( r = 84 \), \( w = 89 \), and \( T = 87 \). We will use the formula \( y=3T - r - w \) from part (a).

Step2: Substitute the values

Substitute \( T = 87 \), \( r = 84 \), and \( w = 89 \) into the formula:
\( y=3\times87-84 - 89 \)

Step3: Calculate the result

First, calculate \( 3\times87 = 261 \). Then, \( 261-84=177 \), and \( 177 - 89 = 88 \).

Answer:

\( y = 3T - r - w \)

Part (b)