Difference between revisions of "2018 AMC 8 Problems/Problem 13"
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Say Laila gets a value of <math>x</math> on her first 4 tests, and a value of <math>y</math> on her last test. Thus, <math>4x+y=410.</math> | Say Laila gets a value of <math>x</math> on her first 4 tests, and a value of <math>y</math> on her last test. Thus, <math>4x+y=410.</math> | ||
| − | The value <math>y</math> has to be greater than <math>82</math>, because otherwise she would receive the same score on her last test. Additionally, the greatest value for <math>y</math> is <math>98</math> (as <math>y=100</math> would make <math>x</math> as a decimal), so therefore the greatest value <math>x</math> can be is <math>98</math>. As a result, only <math>4</math> numbers work, <math>86, 90, 94</math> and <math>98</math>. Thus the answer is <math>\boxed{\textbf{(A) }4}</math>. | + | The value <math>y</math> has to be greater than <math>82</math>, because otherwise she would receive the same score on her last test. Additionally, the greatest value for <math>y</math> is <math>98</math> (as <math>y=100</math> would make <math>x</math> as a decimal), so therefore, the greatest value <math>x</math> can be is <math>98</math>. As a result, only <math>4</math> numbers work, <math>86, 90, 94</math> and <math>98</math>. Thus, the answer is <math>\boxed{\textbf{(A) }4}</math>. |
==Video Solution by OmegaLearn== | ==Video Solution by OmegaLearn== | ||
Revision as of 05:27, 1 January 2023
Problem
Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila's score on the last test?
Solution
Say Laila gets a value of 
on her first 4 tests, and a value of 
on her last test. Thus, 
The value has to be greater than 
, because otherwise she would receive the same score on her last test. Additionally, the greatest value for is 
(as 
would make as a decimal), so therefore, the greatest value can be is . As a result, only 
numbers work, 
and . Thus, the answer is 
.
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=3251
~ pi_is_3.14
Video Solutions
~savannahsolver
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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. 
