Ty recieved test grades of 74%, 76%, 76%, 74%, and 82%. What grade would he need to make on the sixth test to get a C if a C is at least 75% but less than 80% ? is it possible for Ty to get an A for his test average (at least 90%)?
average of six tests = ( x1 + x2 + x3 + x4 + x5 + x6 ) / 6 =
In this case:
( 74 + 76 + 76 + 74 + 82 + x6 ) / 6 = ( 382 + x6 ) / 6
To get a C:
75 < ( 382 + x6 ) / 6 ≤ 80
1.
75 < ( 382 + x6 ) / 6
Multiply both sides by 6
450 < 382 + x6
Subtract 382 to both sides
68 < x6
x6 > 68
2.
( 382 + x6 ) / 6 ≤ 80
Multiply both sides by 6
382 + x6 ≤ 480
Subtract 382 to both sides
x6 ≤ 98
To get a C Ty need to score 68% to 98% points.
To get a A:
( 382 + x6 ) / 6 ≥ 90
Multiply both sides by 6
382 + x6 ≥ 540
Subtract 382 to both sides
x6 ≥ 158
Ty´s score on the test can't be ≥ 158%
Isn't possible to get an A.
To determine the grade Ty needs on the sixth test to get a C, we need to find the average of his grades.
Let's calculate the average grade first:
(74% + 76% + 76% + 74% + 82%) / 5 = 382% / 5 = 76.4%
To get a C, Ty's average grade needs to be least 75% but less than 80%. Since his current average is 76.4%, he already meets the minimum requirement for a C.
Now let's assess whether Ty can get an A for his test average. To do this, we need to find the average grade he would need.
Let's assume Ty has completed "n" tests, including the 5 tests mentioned. In order to achieve an average of 90% or higher, the equation we can derive is:
(74% + 76% + 76% + 74% + 82% + x) / (n + 1) ≥ 90%
Simplifying the equation:
(382% + x) / (n + 1) ≥ 90%
382% + x ≥ 90%(n + 1)
x ≥ 90%(n + 1) - 382%
Since the minimum number of tests Ty has already taken is 5, we need to find the largest possible value of "x" to achieve this average. We need to solve for the maximum possible value of "(n+1)".
90%(n + 1) - 382% ≥ 0
90%(n + 1) ≥ 382%
(n + 1) ≥ (382% / 90%)
n + 1 ≥ 4.2444
Since "n" represents the number of tests Ty has already taken, it must be an integer. Therefore, "n + 1" must be the next whole number greater than or equal to 4.2444, which is 5. So, "n" must be at least 4.
To achieve an average of 90% or higher, Ty would need to score 90% or higher on all remaining tests, which is not possible as the highest grade he can get is 100%. Therefore, it is not possible for Ty to get an A for his test average.