2007 AMC 12B Problem 12

A teacher gave a test to a class in which 10\% of the students are juniors and 90\% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test?

\mathrm {(A)} 85\qquad \mathrm {(B)} 88\qquad \mathrm {(C)} 93\qquad \mathrm {(D)} 94\qquad \mathrm {(E)} 98

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.