In your class you have scores of 84 73 74 and 91 on the firs

In your class, you have scores of 84, 73, 74, and 91 on the first four of five tests. To get a grade of C, the average of the first five tests scores must be greater than or equal to 70 and less than 80. Solve an inequality to find the least score you can get on the last test and still earn a C. What score do you need if the fifth test counts as two tests? The least score you need on the last test to get a C is.

Solution

Let the score in the 5th test be x. Then, the average of the first 5 tests is (84+ 73+ 74+91 + x)/5 = (322+x)/5. Since, to get a grade C, the average of the first five scores must be greater than or equal to 70 and less than 80, therefore 70 (322+x)/5 < 80 so that 70 *5 (322+ x ) ¸80 *5 or, 350 (322+x) < 400 or,( 350 – 322) x < 400 - 322 or,28 x < 78. Thus, the score in the 5th test should be greater than or equal to 28 and less than 78 to get a grade C. If the 5th test counts as two tests and x is the score in the 5th test, then, to get a grade C, we must have 70 (322+ 2x)/6 < 80 or, 70 *6 ( 2x + 322) < 80*6 or, 420 (2x +322 )< 480 or,        ( 420 – 322) 2x < (480 – 322) or, 98 2x < 158 or, 98/2 x < 158/2 or, 49 x < 79. Thus, if the 5th test counts as two tests, the score in the 5th test should be greater than or equal to 49 and less than 78 to get a grade C.