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 then became 5:7. How much money did Ethan give to Dakota?

Reiny, you were doing it wrong

To solve this problem, we can break it down into steps:

Step 1: Let's assume Dakota had x dollars. Since Ethan had $8 more than Dakota, Ethan must have had x + $8 dollars.

Step 2: Ethan gave 1/4 of his money to Dakota, which is (1/4)(x + $8) dollars. After giving away this amount, Ethan still has (3/4)(x + $8) dollars.

Step 3: The ratio of Ethan's money to Dakota's money became 5:7. This means that (3/4)(x + $8) divided by x is equal to 5/7. We can set up the equation:

(3/4)(x + $8) / x = 5/7

Step 4: Let's cross-multiply and solve for x:

7(3/4)(x + $8) = 5x
21(x + $8) = 20x
21x + $168 = 20x
x = $168

Step 5: Now that we know x is $168. We can substitute this value back into the equation to find how much Ethan gave away:

(1/4)(x + $8) = (1/4)($168 + $8) = (1/4)($176) = $44

Therefore, Ethan gave $44 to Dakota.

original:

Dakota --- x
Ethan ----- x+8

after give-away:
Dakota --- x + (1/4)(x+8)
= (4x + x+8)/4 = (5x+8)/4
Ethan ---- (3/4)x = 3x/4

3x/4 : (5x+8)/4 = 5 : 7
3x : 5x+8 = 5/7
3x/(5x+8) = 5/7
25x+40 = 21x
we will get a negative value of x, so this question is bogus, not possible