Clariza is looking to achieve a grade of mastery for her Algebra class, which is an average of 85. She has obtained a 90, 82, 84, and an 88. She has her final exam left to take. What grade must she get on her final so that her overall average is the exact grade of 85?(1 point)

Question

Responses

85
85

85.8
85.8

81
81

86

Answer 1

To find out what grade Clariza needs on her final exam to achieve an average of 85, we can set up the following equation.

Let \( x \) be the grade she needs on her final exam. Her current grades are 90, 82, 84, and 88.

First, we calculate her current average from these grades:

\[ \text{Current Average} = \frac{90 + 82 + 84 + 88}{4} = \frac{344}{4} = 86 \]

Now, to find out what she needs to average 85 over 5 exams (4 current grades + 1 final), we set up the following equation:

\[ \frac{90 + 82 + 84 + 88 + x}{5} = 85 \]

Now substitute the total of the known grades:

\[ \frac{344 + x}{5} = 85 \]

Next, multiply both sides by 5 to eliminate the fraction:

\[ 344 + x = 425 \]

Now, subtract 344 from both sides to solve for \( x \):

\[ x = 425 - 344 \] \[ x = 81 \]

So, Clariza must score 81 on her final exam to achieve an overall average of 85.

Therefore, the answer is 81.