Question 119438
You earned the following scores on five science tests: 75,82,90,84, and 71. You want to have an average score of at least 80 after you take the sixth test.
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a. Write and solve an inequality to find the possible scores that you can earn on your sixth test in order to meet your goal.
:
Let x = the required score to have an average of at least 80
{{{(75 + 82 + 90 + 84 + 71 + x)/6}}} => 80
:
Multiply equation by 6 to get rid of the denominator, add up the scores
402 + x = 6(80)
x => 480 - 402
x => 78 required for at least an 80
:
b. the greatest score you can earn on a test is 100. Is it possible for you to have an average score of 90 after the sixth test? Explain you reasoning.
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Not possible, none of the 5 scores are above 90
:
To confirm this, you can use the above equation: substitute 100 for x and see what the average is
{{{(402 + 100)/6}}} = 83.67