Question

Ada, Betty, Chris and David have $45 in total Ada gota 52 fromBetty, Chris tripleshis money and Davids money is cut by hall four of them have the same amount. Initially Ada has?​

Answer 1

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:

$x + y + z + w = 45$

Ada gets 2 from Betty, hence:

$x + 2 = y - 2$

$x = y - 4$

$y = x + 4$

Chris triples his money and David's money is cut by half four of them have the same amount, hence:

$x + 4 = y = 3z = \frac{w}{2}$

Then:

$3z = x + 4$

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

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

$w = 2x + 8$

Solving for w, we find Ada's initial amount.

$x + y + z + w = 45$

$x + x + 4 + \frac{x + 4}{3} + 2x + 8 = 45$

$4x + 12 + \frac{x + 4}{3} = 45$

$12x + 36 + x + 4 = 45$

$13x = 5$

$x = \frac{5}{13}$

$x = 0.385$

Initially, Ada has $0.385.

A similar problem is given at brainly.com/question/6120515