student scored 85 in her Algebra class before she took the End of Course Exam (the EOC). The student wants her average to be between 80 and 90 inclusive after her EOC is entered into her grades. The EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade. Write and solve a compound inequality to find the possible score she will need to make on the EOC to get the average she wants for her final grade in the course.(1 point)
Responses
80 ≤85 + 85 +85 +85 + x5 ≤ 90
; 85 ≤ x ≤ 110
80 ≤85 + 85 +85 +85 + x5 ≤ 90
; 85 ≤ x ≤ 110
80 <85 + 85 +85 +85 + x5 < 90
; 85 < x < 110
80 <85 + 85 +85 +85 + x5 < 90
; 85 < x < 110
90 ≤85 + 85 +85 +85 + x5 ≤ 80
; 110 ≤ x ≤ 80
90 ≤85 + 85 +85 +85 + x5 ≤ 80
; 110 ≤ x ≤ 80
90 <85 + 85 +85 +85 + x5 < 80
; 110 < x < 85
The correct answer is:
80 ≤ 85*4/5 + x*1/5 ≤ 90
80 ≤ 68 + x/5 ≤ 90
-12 ≤ x/5 ≤ 22
-60 ≤ x ≤ 110
Therefore, the possible score she will need to make on the EOC to get the average she wants is between -60 and 110.