Anna’s scores on her first four quizzes are 78, 86, 90, and 82. What score should Anna get on her fifth quiz so that her mean quiz score is exactly 85?(1 point)

Question

Responses

93
93

89
89

87
87

85
85

Answer 1

To find out what score Anna needs on her fifth quiz to achieve a mean of 85, we can set up the equation for the mean:

\[ \text{Mean} = \frac{\text{Total of all scores}}{\text{Number of scores}} \]

In this case, we want the mean of the five scores to be 85. Let \(x\) be the score on the fifth quiz. The total of the first four quizzes is:

\[ 78 + 86 + 90 + 82 = 336 \]

Now, we can set up the equation:

\[ \frac{336 + x}{5} = 85 \]

To get rid of the fraction, we can multiply both sides by 5:

\[ 336 + x = 425 \]

Now, we solve for \(x\):

\[ x = 425 - 336 \] \[ x = 89 \]

So, Anna needs to score 89 on her fifth quiz to achieve a mean score of exactly 85.

Thus, the correct answer is:

89.