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# Charlie math average for 3 tests is between 85 and 90 If he scored 8 points more on the second test than on the first test and 5 points less on the third test than on the first test. 1st test score?

Updated: 4/28/2022

Wiki User

12y ago

To solve this question, set up a few variables and equations. let A represent the first test, b the second test, and c the third test.

Therefore,

A + 8 = B

A - 5 = C.

We know that the average is between 85 and 90, therefore, the sum of the three values must be between 255 and 270 (multiply 3 by both 85 and 90).

Therefore,

(A) + (A + 8) + (A - 5) = *Some number between 255 and 270* (Bit informal, but its fine for now)

Therefore, it also equals 3A + 3 = *Some number between 255 and 270*

From here, find a number within that range that is divisable by 3, you will find that 261 fits perfectly. However, you will need to use 264 since we will eventually subtract 3 from it. (As you will see in a second).

So, by doing basic algebra, we will see that A = 87.

3A + 3 = 264

3A = 261

A = 87

From there, you can then substitute for B and C.

B must equal 95 and c must equal 82.

If you find the average of the three

(87 + 95 + 82)/3

you will c that it equals 88.

So, the first test was an 87, the second a 95, and the third an 82.

*I believe there may be multiple solutions to this problem, but this one does work*

Wiki User

12y ago

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Q: Charlie math average for 3 tests is between 85 and 90 If he scored 8 points more on the second test than on the first test and 5 points less on the third test than on the first test. 1st test score?
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