Expert: Scott A Wilson - 12/22/2010

Question
You earned the following scores in science:75,82,90,84, and 71. You want to have an average score of at least 80 after your sixth test.
a. write and solve an inequality to find the possible scores that you can earn on your sixth test in order to meet your goal.
b. the greatest score that you can earn on your test is 100. Is it possible for you to have an average score of 90 after six tests? Explain why or why not.

Answer
a.  Note that we would need (75+82+90+84+71+x)/6 >= 80.
First, multiply both sides be 6, giving 75+82+90+84+71+x >= 480.

To solve, add 75, 82, 90, 84, and 71 together, then subtract that value from both sides.
The gives the minimum value of x.

b. The sum of the numbers is a little over 400.  To have an average over 90,
adding the next score would have to make the total at 6*90 = 540, so it would not be possible,
since 540 - 400 = 140, and the maximum is 100.

Another way to test it is just compute the sum with 100 as the last score,
and the average will come out to be less than 90.