solve an inequality

Question

In your​ class, you have scores of 84, 92, 83 and 89 on the first four of five tests. To get a grade of

Upper B, the average of the first five tests scores must be greater than or equal to

80 and less than 90.

a.	Solve an inequality to find the range of the score that you need on the last test to get a upper b
b.	What score do you need if the fifth test counts as two​ tests?

Answer 1

a) If you get a score of X on the fifth test, your final average score will be the total of all the scores, divided by 5,or (84+92+83+89+X)/5

The inequality for part a is 80<= (84+92+83+89+X)/5 < 90 Multiplying all three sides by 5 and combining terms gives us: 400<= 348 + X < 450

We can subtract 348 from all three parts:

52<= X < 102

b) To solve this problem when the last test is worth two tests, the unknown becomes 2X, and the total now acts like the average of 6 tests.

So the inequality becomes: 80 <= (348 + 2X)/6 < 90

Use the same steps from part a to solve again for X

Answer 2

Upper b=400points.

84+92+83+89=348 need 52 points

Need 480 so #5 is to be 132 points. Or 66*2?