Working with linear transformations.

Raw scores on behavioral tests are often transformed for easier comparison.  A test of reading ability has mean 75 and standard deviation 10 when given to third graders.  Sixth graders have a mean score of 82 and a standard deviation of 11 on the same test.  To provide separate norms for each grade, we want scores in each grade to have a mean of 100 and a standard deviation of 20.  What linear transformation will change sixth grade scores x into new scores xnew= a+bx that have the desired mean and standard deviation? (Use b>0 to preserve the order of the scores.)