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Q: The sum of two numbers is 64 and the difference is 6. What are the numbers?

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Let the smaller number be y. Then the larger number is 4y + 9 The sum of the numbers is 64 so ==> y + (4y + 9) = 64 ==> 5y + 9 = 64 ==> 5y = 55 ==> y = 11 so the other number of 53. 11 and 53 are the two numbers

This one will not give pretty numbers, but maybe it's worded wrong, because if it was 32 and -2 then the sum is 30 and product is -64. If you had -32 and +2, then product is -64 and sum is -30. You can solve it as a quadratic: Let p & q be the two numbers: p*q = 64, and p+q=30. rearrange: q = 30-p, and substitute: p*(30-p) = 64: 30*p - pÂ² =64. - pÂ² + 30*p - 64 = 0 [or] pÂ² - 30*p + 64 = 0

8 and 8