The minimum score needed is 95.00 and the maximum score needed is 182.00.
The student's goal is to average a B+ on tests, which is between 86% and 90%. So far, they have scored an 83, 91, and an 83. To find the minimum score they need on the 4th test to stay in the B+ range, we can use the following steps:
Calculate the total number of points they have earned so far: 83 + 91 + 83 = 257
Multiply their desired average by the number of tests to find the total number of points they need to average a B+: 88 * 4 = 352
Subtract the total number of points they have earned so far from the total number of points they need to average a B+: 352 - 257 = 95
This is the number of points they need to earn on the 4th test to average a B+: 95
Divide this number by the number of points on the 4th test to find the minimum score they need: 95 / 100 = 0.95
Convert this decimal to a percentage: 0.95 * 100% = 95%
Therefore, the student needs to score at least 95% on the 4th test to stay in the B+ range.
To find the maximum score they need on the 4th test to stay in the B+ range, we can use the same steps, but we add one point to their desired average in step 3. This is because the highest score they can get on the 4th test is 100%, so we need to make sure that they can still average a B+ even if they get a perfect score on the 4th test.
Following the steps above, we find that the maximum score they need on the 4th test is 182%.
Therefore, to stay in the B+ range, the student must score between 95% and 182% on the 4th test.