SOLUTION: A student completes three assessment tasks and receives marks of 25, 15 and 12. She completes a fourth assessment task and achieves an overall average (mean) of 14.5 for the four t
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Question 587818: A student completes three assessment tasks and receives marks of 25, 15 and 12. She completes a fourth assessment task and achieves an overall average (mean) of 14.5 for the four tests?
a) Assuming that x is the result she obtained on the fourth assessment task, write the information given as an algebraic equation.
You can put this solution on YOUR website! The total of her four scores is the sum of the three known scores (25 + 15 + 12) plus x, her unknown score on the fourth assessment task. If you divide that total by 4 (which is the number of scores) you will get the average score on the four assessment tasks. The problem tells you that the average score is 14.5
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So let's set this up as an equation. Begin by writing the sum of the four scores:
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Divide that sum by 4 to find the average:
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And since we know that the average is 14.5 we can set this equal to 14.5:
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Now we can solve this for x. Begin by adding the first three scores of 25, 15, and 12 to get a total of 52. This makes the equation become:
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Then we can get rid of the denominator 4 on the left side by multiplying both sides of the equation by 4 as follows:
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On the left side, the 4 in the numerator cancels with the 4 in the denominator, and on the right side the product of 4 times 14.5 is 58. This reduces the equation to:
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Next you can get rid of the 52 on the left side by subtracting 52 from both sides to get:
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That's the answer to this problem. She scored 6 on the fourth assessment task.
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So, if she scored a 6 on the fourth assessment task, the resulting average should be 14.5.
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Let's check that. By scoring an 6 on the final assessment task, the four scores become 25 + 15 + 12 + 6. Add these 4 scores and the total is 58. Then find the mean by dividing the total 58 points by 4 and the answer is 14.5, so the answer checks.
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Hope this helps you to understand the problem (and also see that she didn't prepare enough so that she did well on the fourth assessment task).
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