SOLUTION: Different Weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the

Algebra ->  Inequalities -> SOLUTION: Different Weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the      Log On


   

Question 158017: Different Weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put Wendy’s average between 70 and 79 inclusive?


Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=Midterm
y=FinalExam
Let's start with an average of 70 (MIN) first:
Given x=48
%282%2F3%29x%2B%281%2F3%29y=70
%282%2F3%29%2848%29%2B%281%2F3%29y=70
%2896%2F3%29%2B%281%2F3%29y=70
%281%2F3%29y=70-%2896%2F3%29=70-32=38, cross multiply
y=%2838%29%283%29=114, MINIMUM SCORE on Final Exam
Next with an average of 79 (MAX): Given x=48
%282%2F3%29x%2B%281%2F3%29y=79
%282%2F3%29%2848%29%281%2F3%29y=79
%281%2F3%29y=79-%2896%2F3%29=79-32=47, cross multiply
y=3%2A47=141, MAX SCORE on Final Exam
Therefore:To have an average of 70-79 inclusive, he should have a final score of 114-141 inclusive.
Check it out by substituting 1st y=114, 2nd y=141 to the above eqn and you'll get an average of 70 and 79 inclusive.
thank you,
jojo