SOLUTION: Jack needs to earn a C in his sociology class. His current test scores are 67,72,81, and 75. His final exam is worth 3 test scores. In order to earn a C, Jack's average must lie

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Jack needs to earn a C in his sociology class. His current test scores are 67,72,81, and 75. His final exam is worth 3 test scores. In order to earn a C, Jack's average must lie       Log On


   

Question 572412: Jack needs to earn a C in his sociology class. His current test scores are 67,72,81, and 75. His final exam is worth 3 test scores. In order to earn a C, Jack's average must lie between 70 and 79, inclusive. What range of scores can Jack recieve on the final exam and earn a C in the course? Please help! I am desperate.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jack needs to earn a C in his sociology class. His current test scores are 67,72,81, and 75.
His final exam is worth 3 test scores.
In order to earn a C, Jack's average must lie between 70 and 79, inclusive.
What range of scores can Jack receive on the final exam and earn a C in the course?
:
Let x = the required test score on the exam
:
Exam is worth 3 scores (3x), therefore we will be dealing with total of 7 test scores
:
%283x+%2B+67+%2B+72+%2B+81+%2B+75%29%2F7 = 70, his minimum for a C average
%283x+%2B+295%29%2F7 = 70
Multiply both sides by 7
3x + 295 = 7(70)
3x + 295 = 490
3x = 490 - 295
3x = 195
x = 195%2F3
x = 65 min score on the exam for have a 70 average
:
Do the same with to find test score for 79 average
%283x+%2B+67+%2B+72+%2B+81+%2B+75%29%2F7 = 79, his minimum for a C average
%283x+%2B+295%29%2F7 = 79
Multiply both sides by 7
3x + 295 = 7(79)
3x + 295 = 553
3x = 553 - 295
3x = 258
x = 258%2F3
x = 86 score on the exam for have a 79 average
:
The range of test scores would be from 65 to 86 for a 70 to 79 average