Jacob has a mean score of 78 after his first four math tests. He wants to make a B, or an average of 80, in math. What does he need to score on the fifth test to have a mean score of 80?A.
82
B.
88
C.
94
D.
108
Let x be the score on the fifth test.
The sum of the scores on the first four tests is 78 * 4 = <<78*4=312>>312.
The total sum of the scores after the fifth test is 312 + x.
The mean score after the fifth test is (312 + x) / 5 = 80.
So 312 + x = 400.
Therefore, the score Jacob needs to get on the fifth test is x = 400 - 312 = 88.
Thus, the answer is B.
To find out what Jacob needs to score on the fifth test to have a mean score of 80, we can use the formula for the mean:
Mean = (Sum of all scores) / (Number of scores)
Since Jacob has already taken 4 tests and has a mean score of 78, we can determine the sum of these 4 scores by multiplying the mean by the number of scores:
Sum of 4 scores = Mean * Number of scores
Sum of 4 scores = 78 * 4
Sum of 4 scores = 312
Now, if Jacob wants to have a mean score of 80 after the fifth test, we can calculate the sum of all 5 scores:
Sum of 5 scores = Mean * Number of scores
Sum of 5 scores = 80 * 5
Sum of 5 scores = 400
To determine the score Jacob needs on the fifth test, we subtract the sum of the 4 scores Jacob has already achieved from the sum of all 5 desired scores:
Score needed on the fifth test = Sum of 5 scores - Sum of 4 scores
Score needed on the fifth test = 400 - 312
Score needed on the fifth test = 88
Therefore, Jacob needs to score 88 on the fifth test in order to have a mean score of 80. So, the correct answer is B. 88.
To figure out what score Jacob needs on his fifth test to have a mean score of 80, we can use the formula for the mean:
Mean = (Sum of scores) / (Number of scores)
We know that Jacob's mean score after the first four tests is 78. So we can write this equation:
78 = (Sum of the first four scores) / 4
To find the sum of the first four scores, we can multiply the mean by the number of scores:
78 * 4 = Sum of the first four scores
Simplifying this equation, we get:
312 = Sum of the first four scores
Now, let's assume Jacob scores a "x" on his fifth test. To find his mean score after the fifth test, we can use the formula for the mean again:
80 = (Sum of all five scores) / 5
To find the sum of all five scores, we can substitute the sum of the first four scores and the score of the fifth test into this equation:
80 = (312 + x) / 5
To isolate "x", we can multiply both sides of the equation by 5:
400 = 312 + x
Now, let's solve for "x" by subtracting 312 from both sides:
400 - 312 = x
x = 88
Therefore, Jacob needs to score 88 on his fifth test to have a mean score of 80. So the correct answer is B.