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Let's call the smaller number n and the larger (n+9). Making the second statement into an equation:

5n = 3(n+9) + 7

5n = 3n + 27 + 7

5n = 3n + 34

2n = 34

n = 17 and n+9 = 26

Check: Do the number fit the problem?

5 * 17 = 7 + 3 * 26

85 = 7 + 78 TRUE, the numbers 17 and 26 are a valid solution for the problem.

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Q: The difference of two integers is 9. Five times the smaller is seven more than three times the larger - find the numbers?
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