SOLUTION: In a certain course, students take 8 exams that are graded on a scale from 0 to 100, inclusive. Jacob received an average score of 65 on his first 4 exams. What is the lowest score

Question 1045511: In a certain course, students take 8 exams that are graded on a scale from 0 to 100, inclusive. Jacob received an average score of 65 on his first 4 exams. What is the lowest score he can receive on his 5th exam and still be able to score an average of 75 for all 8 exams?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if his overall score need to be an average of 75 for each of the 8 tests, than the total score for all 8 tests needs to be 8 * 75 = 600.

he already got an average of 65 for the first 4 tests.

that's a total of 4 * 65 = 260 for the first 4 tests.

to get an average of 75 on all 8 tests, he needs to get a total of 8*75 = 600.

subtract 260 from 600 and you get 340.

that's the total he needs to get on the last 4 tests.

assuming he got 100 on each of test 6,7,8, then that leaves 40 for test 5.

that's the least he can get on test 5 and still be able to get an average of 75 for all 8 tests.

you've got 260 for the first 4 tests plus 300 for the last 3 tests which leaves 40 for the fifth test.

anything less than 40 on the fifth test and it will be impossible for him to score an average of 75 on all 8 tests.

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