In Wilbur's math class, his grade is based on the average score of six tests, each worth 100 points. Wilbur always worries about his grade. He knows that his average on the first four tests is 88.5. What is the lowest average he could get on his next two tests and still average 90 overall?
If you think about the 6 tests as one big test, there are 600 marks overall. Wilbur got 88.5 * 4 = 354 out of the first 400 marks.
Now, to get 90 overall, you need 0.9*600 = 540 out of 600 marks. Now, 540-354 = 186, so that he must get 186 out of the next 200 marks. This translates to an mean of 186/2 = 93 for each of the last 2 tests.
To find the lowest average Wilbur could get on his next two tests and still average 90 overall, we need to set up an equation.
Let's denote the average score on his next two tests as "x". We know that his average on the first four tests is 88.5. So the sum of his scores on the first four tests is 88.5 * 4 = 354.
If the average of all six tests is 90, then the sum of all six test scores will be 90 * 6 = 540.
To find the minimum average for the last two tests, we need to find the lowest possible sum of scores for those tests. Since each test is worth 100 points, the sum of the last two test scores should be the lowest value possible.
Let's denote the sum of the last two test scores as "y". We can then set up the equation:
y + 354 = 540
Now, let's solve for "y":
y = 540 - 354
y = 186
So, the sum of the last two test scores must be 186. Since each test is worth 100 points, the lowest average for the last two tests would be 186 / 2 = 93.
Therefore, the lowest average Wilbur could get on his next two tests and still average 90 overall is 93.