Question

You are taking a Math class, where your grade is determined by your performance in 5 tests. The maximum score on each test is 100. Your first 4 test scores have been 63,80,90 and 85. To receive a B in the class, the average of the five test scores must be greater than or equal to 80 and strictly smaller than 90. If only integer test scores are allowed, how many different test scores could you receive for the last test and get a grade of B?

Answer 1

We can write our average as \(\dfrac{63+80+90+85+x}5\) and we have the bounds:$$80\le\frac{63+80+90+85+x}5\lt90\\400\le63+80+90+85+x\lt450\\400\le318+x\lt450\\82\le x\lt132$$Because the maximum score is \(100\), we really only have \(82\le x\le 132\) as possible values of \(x\) and thus our answer is merely the number of integers from \(82\) to \(100\) inclusive, i.e. \(100-82+1=18+1=19\)

Answer 2

err \(82\le x\le 100\) as our possible values of \(x\)