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

To determine the amount Ethan gave to Dakota, initial amounts for Ethan and Dakota are calculated using algebraic expressions. The given ratio of 5:2, after Ethan's transfer, provides an equation for solving the initial amounts.

Step-by-step explanation:

To solve for how much money Ethan gave to Dakota, let's define Ethan's initial amount of money as E and Dakota's amount as D. Since Ethan had $8 more than Dakota, we can express this as E = D + $8. After Ethan gave 1/4 of his money to Dakota, Ethan was left with 3/4 of E, and Dakota had D + (1/4)E. The new ratio of Ethan's money to Dakota's money is 5:2, which can be represented by the equation (3/4)E / (D + (1/4)E) = 5/2.

By solving this equation for E and D, we find the initial amounts for Ethan and Dakota, and from there, we can calculate 1/4 of Ethan's initial amount, which is the amount he gave to Dakota.

Answer 2

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
`(1)/(4)` of money to the Dakota i.e
`(1)/(4)` of ( x + $8)

Amount available with Dakota = x +
`[(1)/(4)*(x+8)]`

=
`(5)/(4)x+2`

Amount available with Ethan = (x + $8) -
`[(1)/(4)*(x+8)]`

=
`(3)/(4)x+6`

Now,

`((3)/(4)x+6)/((5)/(4)x+2)=(5)/(2)`

or

`((3x+24)/(4))/((5x+8)/(4))=(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