Expert: Josh - 1/26/2011

Question
I am having trouble with the formation of the inequality and which numbers to use to solve this problem. I am not strong in algebra and appreciate any help. I have the answer to the problem already but i would like to learn the steps and how to solve to get the right answer. Here is my math problem: Cindy has scores of 72, 82, 83, and 89 on her biology tests. Use a compound inequality to find the range of scores she can make on her final exam to receive a C in the course. The final exam counts as two tests, and a C is received if the final course average is from 70 to 79.

Answer
Hi Dulce,

The key to this is finding an expression for the final course average.
Normally, a simple average is given by the sum of scores, divided by the number of scores.
But here, the final exam is worth twice as much as a regular test. So, we need to double the weight given to the final exam.

As Cindy has already obtained four scores, the final composition of her mark in the subject is given by 72+82+83+89+2*x, where x denotes the score in the final exam [notice that its weight has been doubled]. The average mark in the course is given by M=[72+82+83+89+2*x]/6.

Note: The total score is divided by six since we have five scores, but the final score (from the exam) is worth twice as much.

The range for a grade C is 70 <= M <=79.
Thus, we have 70 <= [326+2x]/6 <= 79.
Multiply throughout by 6, we get
420 <= 326+2x <= 474
94 <= 2x <= 148
47 <= x <= 74