Question

Ethan had $8 more than Dakota. Ethan then gave 1/4 of his money to Dakota. The ratio of money Ethan had to the money Dakota had became 5:2. How much money did Ethan five to Dakota?

Answer 1

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 $\frac{1}{4}$ of money to the Dakota i.e $\frac{1}{4}$ of ( x + $8)

Amount available with Dakota = x + $[\frac{1}{4}\times(x+8)]$

= $\frac{5}{4}x+2$

Amount available with Ethan = (x + $8) - $[\frac{1}{4}\times(x+8)]$

= $\frac{3}{4}x+6$

Now,

$\frac{\frac{3}{4}x+6}{\frac{5}{4}x+2}=\frac{5}{2}$

or

$\frac{\frac{3x+24}{4}}{\frac{5x+8}{4}}=\frac{5}{2}$

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