Amaya’s test scores in algebra 1 are 48 and 61. she has one more test left and wants to earn a d for

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

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  1. Amaya's overall grade will be an average of all the scores. To find the average, we must add up the scores and divide by the number of tests.

    We know 2 of the scores, so we can represent the average as:

    (48+61+x)/3

    Now write the inequality.

    60 <= (109 + x)/3 <= 69

    Now let's find the lower bound to receive a D. First we need to multiply both sides by 3.

    180 <= 109+x

    Now subtract 109.

    71 <= x

    Now let's find the upper bound. Do the same thing but with the 69.

    109+x <= 207

    x <= 98

    So Amaya will receive an overall grade of a D if she scores anywhere from 71 to 98 on the test.

  2. 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]

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