SOLUTION: Marie scored 95, 86, and 89 on three science tests. She wants her average score for 6 tests to be at least 90. What inequality can you write to find the average scores that she can

Algebra ->  Average -> SOLUTION: Marie scored 95, 86, and 89 on three science tests. She wants her average score for 6 tests to be at least 90. What inequality can you write to find the average scores that she can      Log On


   

Question 940642: Marie scored 95, 86, and 89 on three science tests. She wants her average score for 6 tests to be at least 90. What inequality can you write to find the average scores that she can get on her next three tests to meet this goal? Use s to represent the lowest average score.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
she will have a total of 6 scores and their average has to be >= 90
this means their total has to be >= 6 * 90 which means their total has to be >= 540.
if s is equal to the average of the last 3 tests she hasn't taken yet, then 3s is equal to the total of the 3 tests she hasn't taken yet.
the total of the 6 tests is therefore equal to 95 + 86 + 89 + 3s which is >= 540.
simplify this to get 270 + 3s >= 540
subtract 270 from both sides of this equation to get 3s >= 540 - 270 which becomes 3s >= 270.
divide both sides of this equation by 3 to get s >= 90
the average of the last 3 tests has to be >= 90.
you would then get, for all 6 tests:
270 + 270 >= 540 which would become 540 >= 540.
the smallest average on the last 3 tests has to be 90.