# How many audiences at a musical

• MHB
• Johnx1
In summary, using variables for the number of people in the audience (A), males (M), females (F), boys (B), and girls (G), we can solve for the number of people in the audience by setting up the equations G = (3/10)(5/8)A and B = (1/3)(3/8)A, and using the fact that there are 21 more girls than boys (G = B + 21). Solving for A, we get A = 336, which means there are 336 people in the audience.
Johnx1
5/8 of the audience at a musical are females. 3/10 of the females are girls and 1/3 of the males are boys. There are 21 more girls than boys. How many people are there in the audience?

My answer. I'm not sure how to do this.

I know that there are 3/8 males.-------------------------------------------------------------------------------------------------------
In the book they did:

For girls, 3/10 * 5/8 = 3/16 girls (why they multiplied both fractions?)
For boys, 1/3 * 3/8 = 1/8 boys (same, why they multiplied both fractions?)

Then they subtracted 3/16 - 1/8 to find the audience. So there is 1/16 audiences. (why subtract both fractions?)

Lastly, they did 1/16 = 21. So they got an another of 336. (why did they equal it to 21?)

I'm not sure how the book did it.
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Is there an easy way to do this creating an algebraic expression?

We could use variables, although we'll essentially wind up doing what your book did. Let $$A$$ be the number of people in the audience, with $$M$$ being the number of males, $$B$$ the number of boys, $$W$$ the number of women and $$G$$ the number of girls. From the given information, we may write:

$$\displaystyle G=\frac{3}{10}F=\frac{3}{10}\cdot\frac{5}{8}A=\frac{3}{16}A$$

$$\displaystyle B=\frac{1}{3}M=\frac{1}{3}\cdot\frac{3}{8}A=\frac{1}{8}A$$

We know the number of girls is 21 more than the number of boys:

$$\displaystyle G=B+21$$

Hence:

$$\displaystyle \frac{3}{16}A=\frac{1}{8}A+21$$

Multiply through by 16:

$$\displaystyle 3A=2A+336$$

Subtract through by $$2A$$:

$$\displaystyle A=336$$

MarkFL said:
$$\displaystyle G=\frac{3}{10}F=\frac{3}{10}\cdot\frac{5}{8}A=\frac{3}{16}A$$

$$\displaystyle B=\frac{1}{3}M=\frac{1}{3}\cdot\frac{3}{8}A=\frac{1}{8}A$$

We know the number of girls is 21 more than the number of boys:

$$\displaystyle G=B+21$$

Before I posted the question, I did get somewhat to this part, but I didn't put (Girls and Women) and (Boys and Men) into as an Audience.

So I got stuck here $$\displaystyle G=B+21$$

You made it much more sense. Thank you.

## 1. How is the number of audiences at a musical calculated?

The number of audiences at a musical is calculated by counting the number of tickets sold or the number of people who attended the show. This number can also include comped tickets, but does not include no-shows or people who leave early.

## 2. What factors can affect the number of audiences at a musical?

The number of audiences at a musical can be affected by various factors such as the popularity of the show, the size of the theater, the time of year, the marketing and advertising efforts, and the ticket prices.

## 3. Is there a difference between the number of audiences and the number of tickets sold?

Yes, there is a difference between the number of audiences and the number of tickets sold. The number of tickets sold represents the total number of tickets purchased, while the number of audiences is the actual number of people who attended the show.

## 4. How does the number of audiences at a musical impact its success?

The number of audiences at a musical is a key factor in determining its success. A higher number of audiences indicates that the show is popular and has a strong following. This can lead to longer runs and potentially higher revenue for the production.

## 5. Can the number of audiences at a musical be accurately predicted?

While there are forecasting methods that can be used to estimate the number of audiences at a musical, it is not always possible to accurately predict this number. Many factors, such as word of mouth and reviews, can influence the attendance at a show. However, past attendance records and market research can be used to make a reasonable prediction.

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