Katie must take five exams in a math class. If her scores on the first four exams are 77, 79, 95, and 93, what score must Katie get on the fifth exam for her overall mean to be at least 80?
The maximum score on an exam is 100 points. If it is not possible for Katie to achieve the required score on the exam, type np in the answer blank.
Katie needs to get a
x1 = 77
x2 = 79
x3 = 95
x4 = 93
averagge of five exam:
( x1 + x2 + x3 + x4 + x5 ) / 5 = 80
( 77 + 79 + 95 + 93 + x5 ) / 5 = 80
( 344 + x5 ) / 5 = 80 Multiply both sides by 5
344 + x5 = 80 * 5
344 + x5 = 400 Subtract 344 to both sides
x5 = 400 - 344 = 56
Answer:
Greater or equal 56
Proof :
( x1 + x2 + x3 + x4 + x5 ) / 5 =
( 77 + 79 + 95 + 93 + 56 ) / 5 =
400 / 5 = 80
Katie must get 56 or more because ...
1) 77 77
2) 79 79
3) 95 95
4) 93 + 93
-------
344+56= 400
Divide 400 by 5 which equals 80
To solve this problem, we need to find the minimum score Katie needs on the fifth exam in order to achieve an overall mean of at least 80.
The overall mean is the sum of all exam scores divided by the number of exams. In this case, there are five exams.
Let's use the formula to find the minimum score Katie needs:
(77 + 79 + 95 + 93 + x) / 5 >= 80
First, let's simplify the equation:
344 + x >= 400
Now, let's isolate the variable:
x >= 400 - 344
Simplifying further, we get:
x >= 56
Therefore, Katie needs to score a minimum of 56 on the fifth exam in order to achieve an overall mean of at least 80.
Note: Since the maximum score on an exam is 100, Katie can achieve the required score of 56 on the fifth exam.