A 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
80
≤
85
+
85
+
85
+
85
+
x
5
≤
90
; 85 ≤ x ≤ 110
85
≤
x
≤
110
80 ≤85 + 85 +85 +85 + x5 ≤ 90
80
≤
85
+
85
+
85
+
85
+
x
5
≤
90
; 85 ≤ x ≤ 110
85
≤
x
≤
110
80 <85 + 85 +85 +85 + x5 < 90
80
<
85
+
85
+
85
+
85
+
x
5
<
90
; 85 < x < 110
85
<
x
<
110
80 <85 + 85 +85 +85 + x5 < 90
80
<
85
+
85
+
85
+
85
+
x
5
<
90
; 85 < x < 110
85
<
x
<
110
90 ≤85 + 85 +85 +85 + x5 ≤ 80
90
≤
85
+
85
+
85
+
85
+
x
5
≤
80
; 110 ≤ x ≤ 80
110
≤
x
≤
80
90 ≤85 + 85 +85 +85 + x5 ≤ 80
90
≤
85
+
85
+
85
+
85
+
x
5
≤
80
; 110 ≤ x ≤ 80
110
≤
x
≤
80
90 <85 + 85 +85 +85 + x5 < 80
90
<
85
+
85
+
85
+
85
+
x
5
<
80
; 110 < x < 85
110
<
x
<
85
90 <85 + 85 +85 +85 + x5 < 80
90
<
85
+
85
+
85
+
85
+
x
5
<
80
; 110 < x < 85
The possible score she will need to make on the EOC to get the average she wants for her final grade in the course is 85 ≤ x ≤ 110.
To solve this problem, we need to set up a compound inequality.
Let x be the score the student needs to make on the EOC.
The class average counts 4/5 of her grade, so the average of her class scores is (85 + 85 + 85 + 85)/4 = 85.
The EOC counts 1/5 of her overall grade, so the weighted average of her class scores and the EOC score is (4/5 * 85) + (1/5 * x) = 0.8 * 85 + 0.2 * x.
We want the average to be between 80 and 90 inclusive, so we can set up the compound inequality:
80 ≤ 0.8 * 85 + 0.2 * x ≤ 90.
Now, let's solve for x:
80 ≤ 0.8 * 85 + 0.2 * x ≤ 90
80 ≤ 68 + 0.2 * x ≤ 90
80 - 68 ≤ 0.2 * x ≤ 90 - 68
12 ≤ 0.2 * x ≤ 22
Divide all sides of the inequality by 0.2 to isolate x:
12/0.2 ≤ (0.2 * x)/0.2 ≤ 22/0.2
60 ≤ x ≤ 110
So the student needs to score between 60 and 110 on the EOC to get the average she wants for her final grade in the course.
The compound inequality that represents the scores the student needs to achieve on the EOC to have an average between 80 and 90 (inclusive) is:
85 <= (85 + 85 + 85 + 85 + x)/5 <= 90
To solve this compound inequality, we can first simplify it:
425 + x <= 450 <= 5x
Now, we can solve each inequality separately:
425 + x <= 450
x <= 450 - 425
x <= 25
450 <= 5x
450/5 <= x
90 <= x
So, the possible scores the student needs to make on the EOC to achieve her desired average are 25 or above, but not exceeding 90. Therefore, the range of scores she needs to achieve is:
25 <= x <= 90