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

89
89

85
85

87
87

93

Answer 1

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

1. Let \( x \) be the score Anna needs on her fifth quiz.
2. Calculate the current total score from the first four quizzes: \[ 78 + 86 + 90 + 82 = 336. \]
3. The total score with the fifth quiz included will be \( 336 + x \).
4. The mean score after five quizzes must be equal to 85. Therefore, we can set up the equation: \[ \frac{336 + x}{5} = 85. \]
5. Multiply both sides by 5 to eliminate the fraction: \[ 336 + x = 425. \]
6. Solve for \( x \): \[ x = 425 - 336, \] \[ x = 89. \]

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