mikes average on the first four exams in econ 1A is 88. what must he earn on the next exam to raise his overall average to 90
I would start by figuring out how many points he has total so far.
88 average * 4 tests = 352 points.
So then the question is, 352 + how many points ALL divided by 5 tests = 90?
(352+x)/5 = 90
352+x = 450
x = 98.
Now, let's check our work.
352 + 98 = 450
450 / 5 = 90
OR...
We could use basic logic. We could say "Mike needs 2 more points in each test so far to get him to a 90 in each test. There were four tests. 4 test * 2 points a test is 8 points. So on this exam, he needs 90 points, plus 8 points to make up for the others. So he needs a 98."
To determine what score Mike needs on the next exam to raise his overall average to 90, we can use the following equation:
(88 * 4 + x) / 5 = 90
Where x represents the score Mike needs on the next exam.
Let's calculate it step by step:
Step 1: Multiply Mike's average on the first four exams (88) by 4:
88 * 4 = 352
Step 2: Add the result from Step 1 to the score Mike needs on the next exam (x):
352 + x = total score after the next exam
Step 3: Divide the total score after the next exam by the total number of exams (5) to get the overall average:
(352 + x) / 5 = 90
Step 4: Multiply both sides of the equation by 5 to eliminate the fraction:
352 + x = 450
Step 5: Subtract 352 from both sides to isolate the variable x:
x = 450 - 352
Step 6: Perform the subtraction:
x = 98
Therefore, Mike needs to earn a score of 98 on the next exam to raise his overall average to 90.
To determine what Mike must earn on the next exam to raise his overall average to 90, we need some additional information. Specifically, we need to know the weight or percentage that each exam contributes to his overall average. Once we have that information, we can calculate the required score on the next exam.
Let's consider a few scenarios:
Scenario 1: All exams carry equal weight:
If all four exams in econ 1A carry equal weight, then each exam contributes 25% (100% divided by 4) to the overall average. Since Mike's current average is 88, he has accumulated a total of (88 * 4) = 352 points. To raise his overall average to 90, he will need a total of (90 * 5) = 450 points. Therefore, he must earn (450 - 352) = 98 points on the fifth exam.
Scenario 2: Exams have different weights:
If each exam in econ 1A carries different weights, we would need to know the specific weight given to the first four exams. For example, if the first exam has a weight of 20%, the second exam has a weight of 25%, the third exam has a weight of 30%, and the fourth exam has a weight of 25%, we can calculate the required score on the fifth exam using a weighted average formula:
(Exam1 * Weight1 + Exam2 * Weight2 + Exam3 * Weight3 + Exam4 * Weight4 + Exam5 * Weight5) / Total Weight = Overall Average
Let's assume the weights for the first four exams are as follows:
- Exam 1: 20%
- Exam 2: 20%
- Exam 3: 25%
- Exam 4: 35%
If Mike's average on the first four exams is 88, we can calculate his total weighted points using the formula:
(88 * 0.20) + (88 * 0.20) + (88 * 0.25) + (88 * 0.35) = Total Weighted Points
Let's say the total weighted points equal X. To find out the required score on the fifth exam, we can rearrange the formula:
(Exam5 * Weight5) = (Overall Average * Total Weight) - X
Finally, divide both sides of the equation by Weight5 to find Exam5:
Exam5 = [(Overall Average * Total Weight) - X] / Weight5
By substituting the given values into the formula, we can calculate the required score on the fifth exam.
Therefore, without knowing the specific weights given to each exam, it is not possible to determine the exact score Mike needs on the next exam to raise his overall average to 90.