Ty received test grades of 73%,82%,73%,77%, and 77%.
a) 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%?
b) Is it possible for Ty to get a B or better for his test average (at least 80%)?
ANSWERS:
To earn a C in the course, Ty must score at least a ( ??? )%
but less than (??? )% on the sixth test.
Please I need to fill the ???? in the parenthesis and solve letter "b"
75 ≤ (73+82+73+77+77+b)/6 < 80
carry on
I don't understand.Please
75 ≤ (73+82+73+77+77+b)/6 < 80
75 ≤ (382+b)/6 < 80 , should be obvious what I did
450 ≤ 382+b < 480 , I multiplied everybody by 6, in the middle that canceled the 6 at the bottom
68 ≤ b ≤ 98, I subtracted 382 from everybody and I am done!
What does my last inequation tell you ?
a. 75 = (73+82+73+77+77+G)/6 < 80.
75 = (382 + G)/6 < 80,
Multiply by 6:
450 = (382+G) <480,
450-382 = G < 480 - 382,
68 = G < 98,
So he will need a grade(G) of at least 68 but less than 98.
b. (73+82+73+77+77+G)/6 = 80.
(382+G)/6 = 80.
G = ?
Yo what
To find the answer to part (a), we need to calculate the minimum and maximum scores Ty can achieve on the sixth test.
a) To earn a grade of "C", Ty's average percentage needs to be at least 75% but less than 80%. Let's first calculate his current average:
Total score = 73% + 82% + 73% + 77% + 77% = 382%
Average score = Total score / Number of tests = 382% / 5 = 76.4%
To maintain a grade of "C" (at least 75%), Ty's overall average must be equal to or greater than 75%. Therefore, the minimum average he can achieve on the sixth test would be 75%.
Minimum score on the sixth test = 75% * 6 (number of tests) - Total score = 75% * 6 - 382% = 450% - 382% = 68%
To get a grade below 80% (less than 80%), Ty's overall average must be less than 80%. Therefore, the maximum average he can achieve on the sixth test would be 79.99%.
Maximum score on the sixth test = 79.99% * 6 (number of tests) - Total score = 79.99% * 6 - 382% = 479.94% - 382% = 97.94%
So, Ty would need to score at least 68% but less than 98% on the sixth test to get a "C" grade.
b) Since Ty's current average is 76.4%, to achieve a B or better (at least 80%), his overall average would need to be 80% or above. Let's calculate the minimum average he would need on the sixth test to achieve this:
Minimum average for a B grade (80%) = 80%
Minimum score on the sixth test = Minimum average for a B grade * 6 (number of tests) - Total score = 80% * 6 - 382% = 480% - 382% = 98%
Therefore, it is not possible for Ty to get a B or better (at least 80%) for his test average, as the minimum score he can achieve on the sixth test is 98%, which is not feasible.
To summarize:
a) To get a "C" grade, Ty would need to score at least 68% but less than 98% on the sixth test.
b) It is not possible for Ty to get a B or better (at least 80%) for his test average.
let T equal the test grade
find the sum of 1st five tests ... call it S
6 * 75% = 450% ... 6 * 80% = 480%
a) 450% ≤ S + T < 480%
b) 480% ≤ S + T