Alicia had some beads. She gave Bernice half of the beads 2 more. Then, she gave half of the remaining beads to Cindy. If Alicia has 9 beads now, how many beads did Alicia have at first? Show steps.

Answer 1

Let x be the number of beads Alicia had at first.

Alicia gave Bernice half of the beads plus 2 more, so Bernice received (x/2) + 2 beads.

After giving Bernice beads, Alicia had x - ((x/2) + 2) beads left.

Alicia then gave half of the remaining beads to Cindy, so Cindy received (x - ((x/2) + 2)) / 2 beads.

After giving beads to Cindy, Alicia had 9 beads left, so:

x - ((x/2) + 2) - ((x - ((x/2) + 2)) / 2) = 9

Solving the equation:

x - (x/2) - 2 - (x - (x/2) - 2) / 2 = 9
2x/2 - x/2 - 2 = 9
x - x/2 - 2 = 9
x/2 = 11
x = 22

Therefore, Alicia had 22 beads at first.

Answer 2

Solve it with a number sentence, don’t use a variable. Use working backwards method

Answer 3

Let's solve the problem using a number sentence and the working backwards method:

1. Alicia currently has 9 beads.
2. Before giving half of the remaining beads to Cindy, Alicia had 2 * 9 = 18 beads.
3. Before giving half of the beads plus 2 more to Bernice, Alicia had 18 * 2 = 36 beads.
4. Therefore, Alicia originally had 36 beads.