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I am new to this site and am looking for some guidance on how I can solve a word problem dealing with compound inequalities. The question is:

Ralph needs to earn a B in his Geology class. His current test scores are 91, 94, 79, and 74. His final exam is worth 6 test scores. In order to earn a B Ralph's average must lie between 80 and 89 inclusive. What range of scores can Ralph receive on the final exam to earn a B in the course?

I just need the first step...I don't know where to start.

Thank you!!!

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2 Answers 2

up vote 1 down vote accepted

Hint: $80 \le \frac{91 + 94 + 79 + 74+ 6x}{6+4} \le 89$

The middle portion is average, note that the exam counts as 6 tests and so the point value total is equivalent to $6+4$ tests.

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HINT: average test scores=(sum test scores/number of test scores). Sum of test scores=(91+94+79+74)+6(final exam score). Number of test scores=current number of tests+weight of final=4+6. Look for the range of final exam score to get a B in the course.

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