mike has an average of 89 on the five tests he has taken so far this semester. what grade must mike earn on the next test to raise his average grade exactly to 90?
5 * 89 = 445
600 * 0.9 = 540
540 - 445 = 95
( x 1 + x 2 + x 3 + x 4 + x 5 ) / 5 = 89 Multiply both sides by 5
x 1 + x 2 + x 3 + x 4 + x 5 = 89 * 5 = 445
( x 1 + x 2 + x 3 + x 4 + x 5 + x 6 ) / 6 = 90
( 445 + x 6 ) / 6 = 90 Multiply both sides by 6
445 + x 6 = 6 * 90 = 540
x 6 = 540 - 445 = 95
To find out the grade Mike needs on the next test to raise his average to 90, we can use the concept of averages. Let's start by calculating the total points Mike has scored on the five tests he has already taken.
Average = Sum of all scores / Total number of tests
Since Mike has an average of 89 and has taken five tests, we can write the equation as:
89 = (Sum of all scores) / 5
To find the sum of his scores, we can multiply both sides of the equation by 5:
445 = Sum of all scores
Now, let's set up the equation to calculate the grade Mike needs on the next test to reach an average of 90. We know that the total number of tests will be 6 after he takes the next test:
90 = (445 + Grade on the next test) / 6
To isolate the grade on the next test, multiply both sides of the equation by 6:
540 = 445 + Grade on the next test
Now, subtract 445 from both sides:
Grade on the next test = 540 - 445 = 95
Therefore, Mike must earn a grade of 95 on the next test to raise his average grade exactly to 90.