SOLUTION: Jeff had an average score of 8 on the 1st two math quizzes. After he took the 3rd quiz his average was 12. If his score on the 3rd quiz was 13 points higher than his score on the 1

SOLUTION: Jeff had an average score of 8 on the 1st two math quizzes. After he took the 3rd quiz his average was 12. If his score on the 3rd quiz was 13 points higher than his score on the 1

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Question 1064087: Jeff had an average score of 8 on the 1st two math quizzes. After he took the 3rd quiz his average was 12. If his score on the 3rd quiz was 13 points higher than his score on the 1st quiz, then what were the three quiz scores?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The key to this problem is the idea that if the average of

numbers is

, then the sum of the

numbers must be

.

So if the average of the first 2 tests is 8, the sum of the scores of the first two tests must be 16. So let

represent the score of the first test and

represent the score of the second test. Now you can say:

Likewise, if the average of the first three tests is 12, then the sum of the first three scores must be 3 times 12, or 36. So:

Finally, we know that the 3rd test score is 13 points more than the first test score, so:

Now you have three linear equations in three variables, so solve for

,

, and

by any convenient means. Given the configuration of the of the third equation, I would first make a substitution. Then I would simplify and solve for

and

by elimination.

John

My calculator said it, I believe it, that settles it

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