Let's determine the score Tyler needs on Test 6 to achieve an average score of 75.
First, let's list the scores he has received so far:
- Test 1: 50
- Test 2: 52
- Test 3: 77
- Test 4: 88
- Test 5: 91
The goal is to find the required score for Test 6 that will bring his average score to 75.
### Step-by-Step Solution
1. Sum of the Scores of the First Five Tests:
Add up the scores of the first five tests:
[tex]\( 50 + 52 + 77 + 88 + 91 = 358 \)[/tex]
2. Desired Average and the Number of Tests:
Tyler wants an average score of 75 across all 6 tests.
3. Formula for Average:
The formula to find the average score is:
[tex]\[
\text{Average} = \frac{\text{Sum of all scores}}{\text{Number of tests}}
\][/tex]
4. Calculate the Total Sum Required for the Desired Average:
Since we know the average should be 75 and there are 6 tests, we can set up the equation to find the total sum of all 6 scores needed:
[tex]\[
75 = \frac{\text{Sum of all scores}}{6}
\][/tex]
Multiplying both sides by 6 to find the sum of all 6 tests:
[tex]\[
\text{Sum of all scores} = 75 \times 6 = 450
\][/tex]
5. Determine the Required Score for Test 6:
We now know the total sum that all 6 tests need to have, and we already have the sum of the first 5 tests:
[tex]\[
\text{Sum of scores for first 5 tests} + \text{Score on Test 6} = 450
\][/tex]
We know the sum of the first 5 tests is 358, so:
[tex]\[
358 + \text{Score on Test 6} = 450
\][/tex]
Subtract 358 from 450 to find the score needed on Test 6:
[tex]\[
\text{Score on Test 6} = 450 - 358 = 92
\][/tex]
### Conclusion
Tyler needs to score 92 on Test 6 to achieve an average score of 75 across his six tests.
