Let's denote the number of adult tickets sold as $ A $ and the number of children's tickets sold as $ C $.

We have two pieces of information:
1. The total number of tickets sold is 540.
2. The total revenue from the tickets is $2864.

We can set up the following system of equations based on this information:

1. $ A + C = 540 $
2. $ 6A + 2C = 2864 $

First, we can solve the first equation for $ C $:

$$ C = 540 - A $$

Next, we substitute this expression for $ C $ into the second equation:

$$ 6A + 2(540 - A) = 2864 $$

Simplify the equation:

$$ 6A + 1080 - 2A = 2864 $$

Combine like terms:

$$ 4A + 1080 = 2864 $$

Subtract 1080 from both sides:

$$ 4A = 1784 $$

Divide both sides by 4:

$$ A = 446 $$

Now that we have the number of adult tickets sold, we can find the number of children's tickets sold by substituting $ A $ back into the first equation:

$$ C = 540 - 446 $$

$$ C = 94 $$

So, the number of adult tickets sold is 446, and the number of children's tickets sold is 94.

Question

Let's denote the number of adult tickets sold as $ A $ and the number of children's tickets sold as $ C $.

We have two pieces of information:
1. The total number of tickets sold is 540.
2. The total revenue from the tickets is $2864.

We can set up the following system of equations based on this information:

1. $ A + C = 540 $
2. $ 6A + 2C = 2864 $

First, we can solve the first equation for $ C $:

$$ C = 540 - A $$

Next, we substitute this expression for $ C $ into the second equation:

$$ 6A + 2(540 - A) = 2864 $$

Simplify the equation:

$$ 6A + 1080 - 2A = 2864 $$

Combine like terms:

$$ 4A + 1080 = 2864 $$

Subtract 1080 from both sides:

$$ 4A = 1784 $$

Divide both sides by 4:

$$ A = 446 $$

Now that we have the number of adult tickets sold, we can find the number of children's tickets sold by substituting $ A $ back into the first equation:

$$ C = 540 - 446 $$

$$ C = 94 $$

So, the number of adult tickets sold is 446, and the number of children's tickets sold is 94.

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