Question

As of a certain​ date, there had been a total of 14 comma 642 performances of two shows on​ Broadway, with 2406 more performances of Show A than Show B. How many performances were there of each​ show?

Answer 1

Let the number of performances of Show B be \( x \). Then, the number of performances of Show A would be \( x + 2406 \).

According to the problem, the total number of performances of both shows is 14,642. We can set up the equation as follows:

\[
x + (x + 2406) = 14642
\]

This simplifies to:

\[
2x + 2406 = 14642
\]

Next, we subtract 2406 from both sides:

\[
2x = 14642 - 2406
\]

Calculating the right side:

\[
14642 - 2406 = 12236
\]

So now we have:

\[
2x = 12236
\]

Dividing both sides by 2:

\[
x = 6118
\]

Now that we have \( x \), we can find the number of performances of Show A:

\[
\text{Show A} = x + 2406 = 6118 + 2406 = 8524
\]

Thus, the number of performances of Show A is 8,524 and the number of performances of Show B is 6,118.

To summarize:
- Performances of Show A: **8,524**
- Performances of Show B: **6,118**