2019 AMC 8
Complete problem set with solutions and individual problem pages
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?
- A.
- B.
- C.
- D.
- E.
Solution 1
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 .
Solution 2
Right now, she scored and points, for a total of points. She wants her average to be for her tests, so she needs to score points in total. This means she needs to score a total of points in her next tests. Since the maximum score she can get on one of her tests is , the least possible score she can get is .
