Andy Has Grades Of 84, 95, And 86 On Three Math Tests

Andy Has Grades Of 84 95 And 86 On Three Math Tests What Grade M

Andy has grades of 84, 95, and 86 on three math tests. What grade must he obtain on the next test to have an average of exactly 90 for the four tests?

To find the required grade on the fourth test, we start by calculating the total sum of all four tests needed to achieve a 90 average. Since the average is the sum of all grades divided by the number of tests, we set up the equation: (sum of 4 grades) / 4 = 90. Multiplying both sides by 4 gives the total sum: (sum of 4 grades) = 360.

Next, we sum the first three grades: 84 + 95 + 86 = 265. Therefore, the grade needed on the fourth test is 360 - 265 = 95. To have an average of exactly 90 across all four tests, Andy must score a 95 on his next test.

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The problem involves calculating the necessary exam score to achieve a desired average. Specifically, Andy has taken three mathematics tests with grades of 84, 95, and 86. The goal is to determine what grade he must earn on the fourth test to attain an overall average of 90 across all four tests.

Understanding averages, also known as the mean, involves summing the individual scores and dividing by the number of tests. The formula for the average (A) is:

A = (sum of all scores) / (number of scores)

In this context, we want:

(84 + 95 + 86 + M) / 4 = 90

where M is the unknown grade Andy needs on the fourth test.

Multiplying both sides by 4 gives:

84 + 95 + 86 + M = 360

Calculating the sum of the known scores yields:

84 + 95 + 86 = 265

Subtracting this from 360 to find M results in:

M = 360 - 265 = 95

Thus, Andy must score a 95 on his next test to have an overall average of 90.

This calculation highlights the importance of understanding how averages function and how to manipulate algebraic expressions to solve real-world problems related to grades and performance metrics.

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