Number - Please help

[Guest]

Dawn, Ann and Megan had 504 beads altogether. Ann gave some of her beads to Megan and the the number of beads Megan had doubled. Megan then gave some of her beads to Dawn and the number of beads Dawn had also doubled. In the end, all of them had the same number of beads. How many beads did Ann have at first?

Note: I have the answer for this question in the book but I still do not understand the working and how they got the answer. Maybe someone here can show a different way to get the answer which I can understand.

[Guest]

Let "x" be the number of beads Dawn had, "y" the number of beads Ann had, and "z" the number of beads Megan had.

"Dawn, Ann and Megan had 504 beads altogether."
So x+ y+ z= 504.

"Ann gave some of her beads to Megan and the the number of beads Megan had doubled."
Since the the number of beads Megan had doubled, Ann gave her z beads. Ann now had y- z beads and Megan had 2z beads.

"Megan then gave some of her beads to Dawn and the number of beads Dawn had also doubled."
So Megan gave x beads to dawn. Megan now had 2z- x beads and Dawn 2x beads

"In the end, all of them had the same number of beads. How many beads did Ann have at first?"
2x= y- z= 2z- x.

2x= y- z, y- z= 2z- x and x+ y+ z= 504 are three equations to solve for x, y, and z..

[Guest]

Dawn, Ann and Megan had 504 beads altogether. Ann gave some of her beads to Megan and the the number of beads Megan had doubled. Megan then gave some of her beads to Dawn and the number of beads Dawn had also doubled. In the end, all of them had the same number of beads. How many beads did Ann have at first?

Note: I have the answer for this question in the book but I still do not understand the working and how they got the answer. Maybe someone here can show a different way to get the answer which I can understand.

[Guest]

How can you expect someone to show a "different" way than your book has without know what way your book showed?

[Guest]

I know this is too late, but I wanted to give a finished solution.

D + A + M = 504, and after all the exchanges each will have the same amount or 504/3 = 168.
A gives M some amount (x) and after that has 168 since no more exchanges are made on A's part, so A- x = 168, or A = 168 + x
M is then going to give some (y) amount to D that doubles the amount D has, and then will equal 168, D = 2y = 168, so y = 84 and therefore D started with 84.
M + x - y = 168 (M received x from A and gave away y to D then no more exchanges were made), substitute y = 84, M + x - 84 = 168, M + x = 252, M and x are the same since the value doubled so 2x = 252, or x = 126, So M started with 126.
Going back to A, A = 168 + x, or A = 168 + 126, A = 294, So A started with 294.

[Angus53]

Solving the system of equations yields the initial number of beads each person had. Ann's initial number of beads, denoted by y, can then be determined from the solution, providing insight into the initial distribution of beads among Dawn, Ann, and Megan.

[Guest]

Dawn, Ann and Megan had 504 beads altogether. Ann gave some of her beads to Megan and the the number of beads Megan had doubled. Megan then gave some of her beads to Dawn and the number of beads Dawn had also doubled. In the end, all of them had the same number of beads. How many beads did Ann have at first?

Note: I have the answer for this question in the book but I still do not understand the working and how they got the answer. Maybe someone here can show a different way to get the answer which I can understand.

Ann had 294 beads.