Inequalities: midterm is 2/3 of grade, final is 1/3 of grade

[nurse]

Hi everyone. I have another dilema. Can someone check my work? It just doesn't look right to me. The question asked was:

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?

What I got was: 70 (less than sign) 48+48+x over 3 (less than sign) 79
210 (less than sign) 96 + x (less than sign) 237 (because I eliminated the 3)
114 (less than sign) x (less than sign) 141

 

[stapel]

For what does "x" stand? What is the reasoning behind your various inequalities? (What kind of keyboard doesn't have the "<" and ">" signs on it?)

Unless there are some other assumptions, I don't think it is numerically possible for her to pass. She got 48% of the 66[sup:1sqecytp]2[/sup:1sqecytp]/[sub:1sqecytp]3[/sub:1sqecytp] points available on the Mid-Term, or 32 points. There are only 33[sup:1sqecytp]1[/sup:1sqecytp]/[sub:1sqecytp]3[/sub:1sqecytp] points remaining for the Final Exam. To get 70 points overall, she'd need to get 38 points, or 38/(33[sup:1sqecytp]1[/sup:1sqecytp]/[sub:1sqecytp]3[/sub:1sqecytp]) = 1.14, or 114%, on the Final.

Sorry!

 

[nurse]

Sorry if I offended the Math Gods by not using a "< or >" sign. After spending EIGHT HOURS looking at this problem and working it over and over again, I was not thinking straight.