The scores

Calculus Level 2

A got $\alpha$ score on the exam, and B got $\beta$ score on the exam, and $\alpha + \beta = 179$ , $\alpha \beta = 8010$ , the scores of A and B are consecutive , and A got a better score than B on the exam, then what is the score of A, and B?

Give the answer like ( $\alpha$ , $\beta$ ).

Note that $\alpha$ , and $\beta$ is the greek letters that can be read as alpha and beta.

And if you got correct, make sure to write your explanation, but it is not required.

I just want to know how if you got correct.

(93, 92)

(88, 87)

(92, 91)

(94, 93)

(90, 89)

(91, 90)

(87, 86)

(89, 88)

2 solutions

Chris Lewis
Feb 15, 2021

We're given more information than we need here; there's no need to use the value of the product.

Since $\alpha$ and $\beta$ are consecutive, and $\alpha$ is larger, we have $\beta=\alpha-1$ . So $\alpha+(\alpha-1)=179$

and $(\alpha,\beta)=\boxed{(90,89)}$ .

We can easily verify that this is correct using the product.

. .
Feb 15, 2021

A score cannot be negative, so the score must be bigger or equal to 0. A score of A is $\alpha$ , and B is $\beta$ , and A's score is better than B's, and the scores are consecutive. Finally, the sum of 2 scores is $179$ , and the multiplies of 2 scores are $8010$ . Then we must find the 2 scores that satisfy the expressions. The scores of ( $\alpha$ , $\beta$ ) is (90, 89), so the answer is $\boxed{ ( 90, 89 ) }$ .

The scores

2 solutions

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