Question

Amaya's test scores in Algebra 1 are 48 and 61. She has one more test left and wants to earn a D for the course, which is from 60-69 inclusive. Write a compound inequality to repesent the situation and solve the inequality to find the range of scores Amaya has to earn to get a D in Algebra 1. Amaya must get greater than or equal to a

Answer 1

The first thing you should do before writing the compound inequation is to know what Amaya's grade point average is.
The average grade for the three exams is:
(48 + 61 + x) / 3
Then, she wants to get a D in the course, then we have two inequations:
(48+61+x)/3 >=60
(48 + 61 + x) / 3 <= 69
The compound inequation is:
60 <= (48 + 61 + x) / 3 <= 69
Solving the compound inequation:
(48 + 61 + x) / 3> = 60
(48 + 61 + x) / 3 = 60
(48 + 61 + x) = 180
x = 180 - 48 - 61 = 71
On the other hand,
(48 + 61 + x) / 3 <= 69
(48 + 61 + x) / 3 = 69
x = 207 - 48 - 61 = 98
answer
60 <= (48 + 61 + x) / 3 <= 69
the range of scores Amaya you have to earn to get to D in Algebra is
[71 - 98]