Answer:
The amount with Dakota = $0.421
The amount with Ethan = $8.421
Step-by-step explanation:
Let the Initial amount with Dakota be 'x'
Therefore,
Amount with Ethan = x + $8
After giving [tex]\frac{1}{4}[/tex] of money to the Dakota i.e [tex]\frac{1}{4}[/tex] of ( x + $8)
Amount available with Dakota = x + [tex][\frac{1}{4}\times(x+8)][/tex]
= [tex]\frac{5}{4}x+2[/tex]
Amount available with Ethan = (x + $8) - [tex][\frac{1}{4}\times(x+8)][/tex]
= [tex]\frac{3}{4}x+6[/tex]
Now,
[tex]\frac{\frac{3}{4}x+6}{\frac{5}{4}x+2}=\frac{5}{2}[/tex]
or
[tex]\frac{\frac{3x+24}{4}}{\frac{5x+8}{4}}=\frac{5}{2}[/tex]
or
2(3x + 24) = 5(5x + 8)
or
6x + 48 = 25x + 40
or
25x - 6x = 48 - 40
or
19x = 8
or
x = $0.421
Hence,
The amount with Dakota = $0.421
The amount with Ethan = x + $8
= $0.421 + $8
= $8.421
