The class average on a math test was 82 and there are 8 students in the class. If seven of the scores are 80, 90, 78, 100, 76, 74, and 82, what must the 8th score be to produce the average of 82?

76

( 80 + 90 + 78 + 100 + 76 + 74 + 82 + x ) / 8 = 82 Multiply both sides by 8

80 + 90 + 78 + 100 + 76 + 74 + 82 + x = 82 * 8

580 + x = 656 Subtract 580 to both sides

580 + x - 580 = 656 - 580

x = 76

this is

band

To find the 8th score that will produce an average of 82, we first need to calculate the sum of all the scores.

We are given that the sum of the scores for the seven students is 80 + 90 + 78 + 100 + 76 + 74 + 82 = 580.

To find the sum of all 8 scores, we can add the 8th score to this sum. Let's call the 8th score x.

So, the sum of all 8 scores is 580 + x.

Since the average is calculated by dividing the sum by the number of values, we have the equation:

(580 + x) / 8 = 82.

To find x, we can multiply both sides of the equation by 8:

580 + x = 656.

Then, we can isolate x by subtracting 580 from both sides:

x = 656 - 580.

Simplifying:

x = 76.

Therefore, the 8th score must be 76 to produce an average of 82.