Difference between revisions of "2012 AMC 8 Problems/Problem 7"
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==See Also== | ==See Also== | ||
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Revision as of 11:26, 13 June 2022
Problem
Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?
Solution 1
Isabella wants an average grade of on her 4 tests; this also means that she wants the sum of her test scores to be at least
(if she goes over this number, she'll be over her goal!). She's already taken two tests, which sum to
, which means she needs
more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all
points on the fourth test. Therefore, the lowest Isabella could have scored on the third test would be
.
Solution 2
Isabella needs to lose a max of . When she got
and
, the max goes down to
. If we get
on her last test, then she will get
on the third test.
Video Solution
https://youtu.be/HISL2-N5NVg?t=3126
~ pi_is_3.14
https://youtu.be/W_BFw23Ca8c ~savannahsolver
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.