After Ian gave 1/4 of his money to Juan, Juan has twice as much money as Ian. What was the ratio of Ian's money to Juans money at fist?

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After Ian gave 1/4 of his money to Juan, Juan has twice as much money as Ian. What was the ratio of Ian's money to Juans money at fist?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Ok so we aren't given any numbers, so we have to make some up to figure it out. Let's give Ian $12. We need to figure out how much Juan has.
Ian gave 1/4 of his money to Juan. 1/4 of $12 is $3 (12/4=3)
Juan now has twice as much money as Ian. Since Ian gave away $3, he now has $9. So double $9 and you get $18. So Juan has $18 at the end.
But the question is asking about in the beginning. And we know Ian gave Juan $3 to get to that amount. So if we subtract $3 from Juan's ending amount, we get what he started with.
$18-$3= $15. Juan started with $15.
so the ratio of the starting amounts of Ian and Juan is $12:$15, which can be simplified to 4:5
The ending ratio would be the same even if you pretended Ian started with $16. He gave 1/4 away which is $4. Ian now has $12. Juan has twice as much, so he has $24, but $4 of those 24 were Ian's. 24-4=20. Juan started with 20, and Ian started with 16. 16:20 simplifies to 4:5
Understand?
Yes! That makes sense!! Thank you very much!!

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