2019 AMC 8 Problems/Problem 7
Shauna takes five tests, each worth a maximum of points. Her scores on the first three tests are , , and . In order to average for all five tests, what is the lowest score she could earn on one of the other two tests?
We should notice that we can turn the information we are given into a linear equation and just solve for our set variables. I'll use the variables and for the scores on the last two tests. We can now cross multiply to get rid of the denominator. Now that we have this equation, we will assign as the lowest score of the two other tests, and so: Now we know that the lowest score on the two other tests is .
Right now, she scored and points, with a total of points. She wants her average to be for her tests so she needs to score points in total. She needs to score a total of points in her tests. So the minimum score she can get is when one of her scores is . So the least possible score she can get is .
Note: You can verify that is the right answer because it is the lowest answer out of the 5. Since it is possible to get 48, we are guaranteed that that is the right answer.
We can compare each of the scores with the average of : , , , ;
So the last one has to be (since all the differences have to sum to ), which corresponds to .
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