SOLUTION: Ingrid scored 65 on her calculus midterm. If her final exam score counts twice as much as her midterm exam, then for what range of scores on her final would she get an average betw

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Question 155351This question is from textbook COLLEGE ALGEBRA
: Ingrid scored 65 on her calculus midterm. If her final exam score counts twice as much as her midterm exam, then for what range of scores on her final would she get an average between 79 and 90? Hint: For this weighted average multiply the final exam by 2 and the midterm score by 1. This question is from textbook COLLEGE ALGEBRA

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Ingrid scored 65 on her calculus midterm. If her final exam score counts twice as much as her midterm exam, then for what range of scores on her final would she get an average between 79 and 90? Hint: For this weighted average multiply the final exam by 2 and the midterm score by 1.

Let X = her score on the final exam:

Then




Average+=+%281%2A65%2B2%2AX%29%2F%281%2B2%29


Average+=+%2865%2B2X%29%2F3

We want:

79%3C=%2865%2B2X%29%2F3%3C=90

Multiply through by 3 to clear of fractions:

3%2A79%3C=65%2B2X%3C=3%2A90

237%3C=65%2B2X%3C=270

Subtract 65 from all three sides:

237-65%3C=2X%3C=270-65

172%3C=2X%3C=205

Divide through by 2

172%2F2%3C=2X%2F2%3C=205%2F2

86%3C=X%3C=102.5

But we have to cut it off at 100, so

86%3C=X%3C=100

Her grade must be greater than or equal to 86.

Note: It is impossible for her to end up with an
average greater than 881%2F3. 

Edwin