SOLUTION: Natalie, Rachel and Winnie were given a box of beads. Natalie took 5/9 of the beads and then put 14 beads back. Rachel took 1/5 of the remaining beads and then put 8 beads back. Wi

Question 1184472: Natalie, Rachel and Winnie were given a box of beads. Natalie took 5/9 of the beads and then put 14 beads back. Rachel took 1/5 of the remaining beads and then put 8 beads back. Winnie then took half of the remaining beads. The rest of the beads in the box were packed equally into 12 bags. There were 26 beads in each bag. How many beads were given to the girls?
Found 3 solutions by ikleyn, Pussy Licker, 54929:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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Natalie, Rachel and Winnie were given a box of beads.
Natalie took 5/9 of the beads and then put 14 beads back.
Rachel took 1/5 of the remaining beads and then put 8 beads back.
Winnie then took half of the remaining beads.
The rest of the beads in the box were packed equally into 12 bags.
There were 26 beads in each bag. How many beads were given to the girls?
~~~~~~~~~~~~~

            There was an error in my previous solution version.
            Thanks to other solvers who noticed it.
            I corrected everything, and now you see a corrected version below.

To make the solution totally clear, I will present the problem's description in steps. (1) Natalie took 5/9 of the beads. (2) then Natalie returned 14 beads back. (3) then Rachel took 1/5 of the remaining beads (4) then Rachel returned 8 beads back (5) then Winnie took half of the remaining beads. (6) then the rest beads were packed. OK, very good. It will help and very much, as you will see from what follows. Now I will solve the problem moving backward. The number of the packed beads is 12*26 = 312. Hence, the number of beads immediately before step 5 was 312*2 = 624. the number of beads immediately before step 4 was 624 - 8 = 616. the number of beads immediately before step 3 was = 770. <<<---=== use equation = 616. the number of beads immediately before step 2 was 770-14 = 756. the number of beads immediately before step 1 was = 1701. <<<---=== use equation = 756. So, the number of beads, which was given to girls was 1701.

Solved ( in a backward manner ) .

///////////

I am happy to have so attentive readers (!)

Answer by Pussy Licker(3)   (Show Source): You can put this solution on YOUR website!
Haga x como el número original de cuentas en la caja.

Natalie tomó 5/9 de las cuentas y luego volvió a poner 14 cuentas --> (4/9)x + 14 perlas restantes.

Rachel tomó 1/5 de las cuentas restantes y luego volvió a colocar 8 cuentas.--> (4/5)((4/9)x + 14) + 8 = (16/45)x + 56/5 + 8 = (16/45)x + 96/5 perlas restantes .

Winnie luego tomó la mitad de las cuentas restantes. --> .5((16/45)x + 96/5) = (8/45)x + 48/5 cuentas restantes.

Entonces quedan (8/45)x + 48/5 cuentas.

El resto de las cuentas de la caja se empaquetaron por igual en 12 bolsas. Había 26 cuentas en cada bolsa. --> ((8/45) x + 48/5) / 12 = 26.

Entonces la ecuación es (8/45)x + 48/5 = 312. Entonces la ecuación es por lo tanto, originalmente hubo "1701" después de resolver.

Answer by 54929(12)   (Show Source): You can put this solution on YOUR website!
The answer by ikelyn is incorrect
Suppose beads : x
1/2[4/5 (4/9x + 14) + 8] = 12 * 26
=> x=1701
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