A math teacher calculates grades as follows:Grade=[2 test averages+quiz average/3] After 3 tests and 2 quizzes your test average is 83 and your quiz average is 89. You took your fourth test today and noticed that your overall average grade has dropped to an 83. What was your score on the fourth test?
To find your score on the fourth test, we can solve the equation using the given information.
Let's assume your score on the fourth test is "x".
According to the grading formula:
Grade = [2 * test averages + quiz average] / 3
Before taking the fourth test, your test average was given as 83 and your quiz average was given as 89.
Now, we can substitute the values into the equation:
83 = [2 * 83 + 89 + x] / 3
To solve the equation for "x", we can follow these steps:
Step 1: Multiply both sides of the equation by 3 to eliminate the fraction:
3 * 83 = 2 * 83 + 89 + x
Step 2: Simplify the equation:
249 = 166 + 89 + x
Step 3: Combine like terms:
249 = 255 + x
Step 4: Subtract 255 from both sides of the equation:
249 - 255 = x
Step 5: Simplify:
x = -6
Therefore, your score on the fourth test is -6. However, it is important to note that a negative score is not possible in this context. It indicates an error or mistake in the calculation or some missing information. Please double-check the given information and the calculations to resolve any discrepancies.
To solve this problem, we can follow these steps:
Step 1: Calculate the total grade before taking the fourth test
- Given test average: 83
- Given quiz average: 89
- Grade formula: Grade = (2 * test averages + quiz average) / 3
- Substitute the given values into the formula:
Grade = (2 * 83 + 89) / 3
Grade = (166 + 89) / 3
Grade = 255 / 3
Grade ≈ 85
Step 2: Calculate the total grade after taking the fourth test
- Given overall average grade: 83
- Grade formula: Grade = (2 * test averages + quiz average) / 3
- Substitute the known average and solve for the fourth test score:
83 = (2 * test averages + 89) / 3
Multiply both sides by 3:
3 * 83 = 2 * test averages + 89
249 = 2 * test averages + 89
Subtract 89 from both sides:
249 - 89 = 2 * test averages
160 = 2 * test averages
Divide both sides by 2:
160 / 2 = test averages
80 = test averages
Therefore, your score on the fourth test was 80.