How would you find the smaller of two numbers given the ratio between their sum, difference and product? I've been struggling with this one for a while. For example: the ratio between the sum, difference and product is 6:4:15 and the numbers are positive integers
2026-04-01 23:33:39.1775086419
Finding the smaller number of two given the ratio between sum, difference and product
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Just looking at the sum and difference, if the unknown numbers are $a,b$, then there is some real $k$ such that $$a+b=6k$$ and $$a-b=4k$$ We can then solve this to get $a=5k, b=k$. Now, the product is $5k^2$, and using the ratio relationship, $$5k^2=15k$$ from which we conclude $k=3$ and hence $a=15, b=3$. A second, less interesting, solution, is $k=0$, which gives $a=b=0$.