I've attempted to solve this problem, but i keep getting inncorect values. can someone explain what i'm doing incorrectly and give me the correct values? (algebra 2)

Call the three numbers (small, medium and large).

Their sum is 16, so we have

The largest is the sum of the other two, so we have

Finally, we know that three times the smaller (3s) is one less than the largest (l+1), so we have

So, we have the following system:

Subtract the second equation from the first:

Use this value for in the third equation to find :

We know that the largest is the sum of the other two, so we have

So, the three numbers are 3, 5 and 8. You can check that they have all the required features:

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