Question

the average, or mean, d, of three exam grades, y, x, and s, is given by the following formula. ( d = \frac{y + x + s}{3} ) (a) solve the formula for s. (b) use the formula in part (a) to solve this problem. on your first two exams, your grades are 85% and 87%: ( y = 85 ) and ( x = 87 ). what must you get on the third exam to have an average of 87%? (a) the formula is ( s = square ).

Explanation:

Part (a)

Step1: Multiply both sides by 3

To isolate the numerator, we multiply both sides of the equation \( D = \frac{y + x + s}{3} \) by 3. This gives us \( 3D = y + x + s \).

Step2: Subtract y and x

Now, we want to solve for \( s \), so we subtract \( y \) and \( x \) from both sides of the equation \( 3D = y + x + s \). This results in \( s = 3D - y - x \).

Step1: Identify the values

We know that \( y = 85 \), \( x = 87 \), and \( D = 87 \). We will use the formula \( s = 3D - y - x \) from part (a).

Step2: Substitute the values

Substitute \( y = 85 \), \( x = 87 \), and \( D = 87 \) into the formula: \( s = 3\times87 - 85 - 87 \).

Step3: Calculate the result

First, calculate \( 3\times87 = 261 \). Then, \( 261 - 85 - 87 = 261 - 172 = 89 \).

Answer:

\( 3D - y - x \)

Part (b)