The sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer. Find the numbers.

# The sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer. Find the numbers.

1. A
8 and 13
2. B
8 and 43
3. C
6 and 23
4. D
7 and 15

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### Solution:

Given that the sum of the squares of two integers is 233 and one integer is 3 less than twice the other integer.
Let the first integer be x and the other integer be $2x-3.$
Now, according to the question, writing the algebraic expression as follows:

Since x is an integer, so
Thus, ${x}{=}{8}{.}$

Therefore, the numbers are 8 and 13.
Hence, option (1) is correct.

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