Question

christine has scored 99, 66, 86, and 66 on her previous four tests. what score does she need on her next test so that her average (mean) is 78?

Explanation:

Step1: Recall the mean formula

The mean formula is $\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}$. Let the score on the fifth - test be $x$. The sum of the scores of the five tests is $99 + 66+86 + 66+x$, and the number of tests is 5, and the mean is 78. So we have the equation $\frac{99 + 66+86 + 66+x}{5}=78$.

Step2: Simplify the numerator of the left - hand side

First, calculate $99 + 66+86 + 66=317$. So the equation becomes $\frac{317+x}{5}=78$.

Step3: Solve for $x$

Multiply both sides of the equation by 5: $317+x=78\times5$. Since $78\times5 = 390$, the equation is $317+x=390$. Then subtract 317 from both sides: $x=390 - 317$.

Answer:

73