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Ah, what a delightful puzzle you have there! To find two numbers that multiply to 120 but add up to 34, we can think of the factors of 120. The numbers are 24 and 5. They multiply to 120 and add up to 34. Happy little numbers, just like happy little trees!
The numbers that multiply to 120 but add to 34 are 15 and 8. This is because 15 multiplied by 8 equals 120, and 15 plus 8 equals 23. Since the question asks for numbers that add to 34, we can adjust these numbers by adding 11 to 15 and subtracting 11 from 8, giving us 26 and 19. These are the two numbers that multiply to 120 and add up to 34.