In math class, a student has an average grade of 85% for five tests so far. What grade must that student earn on the next test to reach an average grade of 90% for all six tests?

90 * 6 = 540

85 * 5 = 425

540 - 425 = 115

It can't be done if the maximum grade for a test is 100.

To find out the grade the student must earn on the next test, we can set up an equation.

Let's denote the grade the student must earn on the next test as x.

The student's average grade for five tests is 85%. So, the sum of the grades for these five tests is (85% * 5) = 425%.

To achieve an average grade of 90% for all six tests, the sum of all six test grades should be (90% * 6) = 540%.

The sum of the grades for the five tests plus the grade for the next test should be equal to the sum of all six test grades:

425% + x = 540%

Now, we can solve for x:

x = 540% - 425%
x = 115%

Therefore, the student must earn a grade of 115% on the next test to reach an average grade of 90% for all six tests. However, it is worth noting that typically, grades are not given above 100%.

To find the grade the student must earn on the next test to reach an average grade of 90% for all six tests, we need to know the total score the student has achieved so far and the total number of tests taken.

Let's say the student has scored a total of X on the five tests.

Therefore, the sum of the scores on the five tests is 5X.

To calculate the total score the student needs to reach an average of 90% for all six tests, we need to find the sum of the scores needed for six tests.

The total score needed for the six tests can be calculated by multiplying the average grade (90%) by the total number of tests (6).

Total score needed = 90% × 6 = 0.9 × 6 = 5.4

Now, to find the grade the student must earn on the next test, we subtract the total score achieved so far (5X) from the total score needed (5.4).

Grade needed on next test = Total score needed - Total score achieved
= 5.4 - 5X

Therefore, the student must earn a grade of 5.4 - 5X on the next test to reach an average grade of 90% for all six tests.