The College Board finds that the distribution of students' SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT Math scores X, which are distributed with mean 445 and standard deviation 106. Scores of children of parents with graduate degrees have SAT Math scores Y, which are distributed with mean 566 and standard deviation 109. One college seeking to have a more equitable standard for evaluating applicant's SAT scores proposes to standardize the SAT scores of its applicants to a common scale for equity. Find numbers, a, b, c, and d, such that a + bX and c + dY both have mean 500 and standard deviation 100.