smc

Question

All students at Adams High School and at Baker High School take a certain exam. The average scores for boys, for girls, and for boys and girls combined, at Adams HS and Baker HS are shown in the table, as is the average for boys at the two schools combined. What is the average score for the girls at the two schools combined? array[t]|c|c|c|c| 4cAverage Scores Category&Adams&Baker&Adams&Baker Boys&71&81&79 Girls&76&90&? Boys&Girls&74&84& array

Accepted Answer

Let the numbers of boys and girls at Adams be (A,a) and the numbers of boys and girls at Baker be (B,b). Then, reading down, we have 71A+76a=74(A+a) and 81B+90b=84(B+b). Reading across, we have 71A+81B=79(A+B). Simplifying each in turn, 3A-2a=0 A=2a/3 and 3B-6b=0 B=2b and 8A-2B=0 4A=B. Thus 3b = 4a, which implies that Adams has 37 of the girls and Baker has 47 of the girls. So the average score for all girls must be 3 76+4 907 = 228+3607 = 84 which is 84