To determine Leon's grade on the fifth test given that his average test grade is 83.8, we can follow these steps:
1. Determine the number of tests:
Leon has taken five tests in total.
2. Calculate the total grade sum required to achieve the average:
Since the average grade is 83.8 and there are 5 tests, the total sum of all test grades should be:
[tex]\[
\text{Total Sum} = \text{Average Grade} \times \text{Number of Tests}
\][/tex]
[tex]\[
\text{Total Sum} = 83.8 \times 5 = 419.0
\][/tex]
3. Sum the grades of the first four tests:
We know the first four grades are:
[tex]\[
\text{Grade 1} = 78
\][/tex]
[tex]\[
\text{Grade 2} = 86
\][/tex]
[tex]\[
\text{Grade 3} = 82
\][/tex]
[tex]\[
\text{Grade 4} = 88
\][/tex]
Then, sum the first four grades:
[tex]\[
\text{Sum of first four grades} = 78 + 86 + 82 + 88 = 334
\][/tex]
4. Calculate the fifth grade:
To find the grade for the fifth test, subtract the sum of the first four grades from the total sum of all grades needed to achieve the average:
[tex]\[
\text{Grade 5} = \text{Total Sum} - \text{Sum of first four grades}
\][/tex]
[tex]\[
\text{Grade 5} = 419.0 - 334 = 85.0
\][/tex]
So, Leon needs to score 85 on his fifth test to achieve an average score of 83.8 across all five tests.
