Answer :
Sure, let's solve this problem step-by-step!
Maria wants an average score of 82 for her math tests by the end of the quarter. She has already completed three tests with scores of 72, 97, and 82. Let's find out what score she needs on her last test to achieve this average.
1. Understand the Desired Mean:
Maria wants her average score to be 82.
2. Calculate the Total Score Needed:
Since there are four tests in total, to find the total score Maria needs to achieve the average of 82, we can use the formula for the average:
[tex]\[
\text{Average} = \frac{\text{Total Sum of Scores}}{\text{Number of Tests}}
\][/tex]
Rearranging for the total sum of scores, we have:
[tex]\[
\text{Total Sum of Scores} = \text{Average} \times \text{Number of Tests} = 82 \times 4 = 328
\][/tex]
3. Calculate the Current Total of Scores:
Maria's scores so far are 72, 97, and 82. The sum of these scores is:
[tex]\[
72 + 97 + 82 = 251
\][/tex]
4. Determine the Score Needed on the Last Test:
Since the total score needed is 328, and she has already scored 251, the score needed on the last test is:
[tex]\[
\text{Score Needed} = 328 - 251 = 77
\][/tex]
Therefore, Maria needs to score 77 on her last test to achieve an average of 82 for the quarter.
Maria wants an average score of 82 for her math tests by the end of the quarter. She has already completed three tests with scores of 72, 97, and 82. Let's find out what score she needs on her last test to achieve this average.
1. Understand the Desired Mean:
Maria wants her average score to be 82.
2. Calculate the Total Score Needed:
Since there are four tests in total, to find the total score Maria needs to achieve the average of 82, we can use the formula for the average:
[tex]\[
\text{Average} = \frac{\text{Total Sum of Scores}}{\text{Number of Tests}}
\][/tex]
Rearranging for the total sum of scores, we have:
[tex]\[
\text{Total Sum of Scores} = \text{Average} \times \text{Number of Tests} = 82 \times 4 = 328
\][/tex]
3. Calculate the Current Total of Scores:
Maria's scores so far are 72, 97, and 82. The sum of these scores is:
[tex]\[
72 + 97 + 82 = 251
\][/tex]
4. Determine the Score Needed on the Last Test:
Since the total score needed is 328, and she has already scored 251, the score needed on the last test is:
[tex]\[
\text{Score Needed} = 328 - 251 = 77
\][/tex]
Therefore, Maria needs to score 77 on her last test to achieve an average of 82 for the quarter.
