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.

would be a great help
Answer by bucky(2189) About Me  (Show Source):
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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25+%2B+15+%2B+12+%2B+x
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Divide that sum by 4 to find the average:
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%2825+%2B+15+%2B+12+%2B+x%29%2F4
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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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%2825+%2B+15+%2B+12+%2B+x%29%2F4+=+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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%2852+%2B+x%29%2F4+=+14.5
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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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%284%2A%2852+%2B+x%29%29%2F4+=+4%2A14.5
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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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52+%2B+x+=+58
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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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x+=+6
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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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