SOLUTION: Prof. W counts his midterm as 2/3 of the grade and his final counts as 1/3 of the grade. Wendy scored a 48 on the midterm. What range of scores would she need to get on the final

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Question 53323This question is from textbook Elementary and Intermediate Algebra
: Prof. W counts his midterm as 2/3 of the grade and his final counts as 1/3 of the grade. Wendy scored a 48 on the midterm. What range of scores would she need to get on the final to put Wendy's average between 70 and 79 inclusive? This question is from textbook Elementary and Intermediate Algebra

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I answered this one yesterday. In case you're the same student and I wasn't clear enough. Let me explain that with a three way inequality, you want to get the variable in the middle all by itself within the rules of algebra. What ever you do to the middle, you have to do at both ends.
I've got to tell you, it doesn't look good for Wendy. It's as if she has three tests and she got a 48 on two of them and hopes to bring her grade up between 22 and 31 points with the last test.
Prof. W's grading says that 2/3*midterm and 1/3*final=grade.
Let the final=x and we have this inequality:
70%3C=%282%2F3%29%2848%29%2B%281%2F3%29x%3C=79
70%3C=+96%2F3%2Bx%2F3%3C=79
70%3C=32%2Bx%2F3%3C=79
70-32%3C=32-32%2Bx%2F3%3C=79-32
38%3C=x%2F3%3C=47
3%2A38%3C=3%2Ax%2F3%3C=3%2A47
114%3C=x%3C=141
Wendy's going to need a lot of bonus points!!!