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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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