Firstly, 4/9 suggest that Caleb has 4 units and Fred has 9 units.

Total = 13 units

But later part of question mentioned that they would have equal amounts of money.

And 13 units is not divisible by 2.

So we should change the fraction by multiplying both numerator and denominator by 2.

4/9 = 8/18

Caleb : 8 units
Fred : 18 units
Total: 26 units

Now if they have equal $, then each has
26 units ÷ 2 = 13 units




So now,

Draw 8 units for Caleb, 18 for Fred.

18 units - 13 units = 5 units

This means Fred has to give 5 units to Caleb such that both have equal $.

So for your 'before' model,draw the transfer of 5 units from Fred to Caleb.

Then for your 'after' model, draw both having 13 units.

And if Fred has to give Caleb $50, this means that $50 = 5 units

And therefore 1 unit = $10. You can label the 5 units transferred as $50.




From here we find their total amount and Caleb's amount

Total = 26 units x $10 per unit = $260
Caleb's amount = 8 units x $10 per unit
= $80

Now, if Caleb is to end up having 1/4 of
Fred's $, then Caleb has 1 part and Fred has 4 parts. Total is 5 parts.


So Caleb would have 1/5 of the total $ in the end.


1/5 x $260 = $52

Or

$260 ÷ 5 = $52

So Caleb will end up having $52.

Amount he must give Fred
= $80 - $52
= $28