Using a system of equations, it is found that initially Ada has $0.385.
For the system, we have that the variables are:
- x is Ada's amount.
- y is Betty's amount.
- z is Chris's amount.
- w is David's amount.
$45 total, hence:
[tex]x + y + z + w = 45[/tex]
Ada gets 2 from Betty, hence:
[tex]x + 2 = y - 2[/tex]
[tex]x = y - 4[/tex]
[tex]y = x + 4[/tex]
Chris triples his money and David's money is cut by half four of them have the same amount, hence:
[tex]x + 4 = y = 3z = \frac{w}{2}[/tex]
Then:
[tex]3z = x + 4[/tex]
[tex]z = \frac{x + 4}{3}[/tex]
[tex]x + 4 = \frac{w}{2}[/tex]
[tex]w = 2x + 8[/tex]
Solving for w, we find Ada's initial amount.
[tex]x + y + z + w = 45[/tex]
[tex]x + x + 4 + \frac{x + 4}{3} + 2x + 8 = 45[/tex]
[tex]4x + 12 + \frac{x + 4}{3} = 45[/tex]
[tex]12x + 36 + x + 4 = 45[/tex]
[tex]13x = 5[/tex]
[tex]x = \frac{5}{13}[/tex]
[tex]x = 0.385[/tex]
Initially, Ada has $0.385.
A similar problem is given at https://brainly.com/question/6120515
