In the first act of a play, all the actors were on stage. The second act opened with 1/2 the actors on stage, and then 5 actors left. After that, 1/2 remaining actors left, and 4 actors remained on stage. How many actors were on stage in the first act?

Question

In the first act of a play, all the actors were on stage. The second act opened with 1/2 the actors on stage, and then 5 actors left. After that, 1/2 remaining actors left, and 4 actors remained on stage. How many actors were on stage in the first act?

Answer 1

first act, number of actors ---- x

2nd act, x/2 on stage, then 5 left
actors remaining x/2 - 5

then 1/2 of those left, leaving (x/2 - 5)/2

but (x/2 - 5)/2 = 4
x/2 - 5 = 8
x/2 = 13
x = 26

Answer 2

Let's solve this step by step:

1. Let's assume the number of actors in the first act is unknown and represented by "x".

2. In the second act, 1/2 of the actors from the first act were on stage. So, the number of actors on stage in the second act is (1/2) * x.

3. After that, 5 actors left the stage. So, the number of actors remaining on stage is (1/2) * x - 5.

4. Finally, 1/2 of the remaining actors left, and 4 actors remained on stage. This gives us the equation (1/2) * ((1/2) * x - 5) = 4.

5. To solve for x, let's simplify the equation step by step. Distribute (1/2) to the terms inside the parentheses: ((1/2) * (1/2) * x) - ((1/2) * 5) = 4.

6. Simplify further: (1/4) * x - 5/2 = 4.

7. Add 5/2 to both sides of the equation: (1/4) * x = 4 + 5/2.

8. Combine the fractions: (1/4) * x = 8/2 + 5/2 = 13/2.

9. We want to isolate x, so we multiply both sides of the equation by 4: x = (13/2) * 4.

10. Multiply: x = 26.

Therefore, there were 26 actors on stage in the first act.

Answer 3

To find the number of actors on stage in the first act, we can work backwards from the information given.

In the second act, after half the actors left and 5 actors left, there were 4 actors remaining on the stage.

Let's denote the number of actors in the first act as 'x'.
In the second act, after half the actors left, there were 1/2 * x actors remaining on stage.
Then, when 5 actors left, there were 1/2 * x - 5 actors remaining on stage.

Finally, after half of the remaining actors left again, there were 4 actors remaining on stage.
This means that 1/2 * (1/2 * x - 5) = 4.

To find the value of x, we can solve this equation step by step.

1/2 * (1/2 * x - 5) = 4
1/4 * x - 5/2 = 4
1/4 * x = 4 + 5/2
1/4 * x = 4 + 10/2
1/4 * x = 4 + 5
1/4 * x = 9
x = 9 * 4
x = 36

Therefore, there were 36 actors on stage in the first act.

In the first act of a play, all the actors were on stage. The second act opened with 1/2 the actors on stage, and then 5 actors left. After that, 1/2 remaining actors left, and 4 actors remained on stage. How many actors were on stage in the first act?

first act, number of actors ---- x

Thanks

Let's solve this step by step:

To find the number of actors on stage in the first act, we can work backwards from the information given.