Adult tickets for a play cost $13 and child tickets cost $10. If there were 22 people at a performance and the theater collected $277 from ticket sales, how many adults and how many children attended the play?

Adult tickets sold = x

Children's tickets sold = y

x + y = 22
13x + 10 y = 277

Solve that pair of equations.
Hint: substitute 22-x for y in the second equation, and solve for x. .

The next step would be

13x + 220 - 10x = 277
3x = 277-220 = 57
Divide both sides by 3 and you have x.
You know how to get y after that.

Adults= 11 30 total

Child- 5

To solve this problem, we can set up a system of equations. Let's define the variables:

Let A represent the number of adult tickets sold.
Let C represent the number of child tickets sold.

From the given information, we have two equations:

Equation 1: A + C = 22 (since there were 22 people at the performance)
Equation 2: 13A + 10C = 277 (since the theater collected $277 from ticket sales)

We can solve this system of equations by using the method of substitution or elimination.

Let's use the method of substitution:

From Equation 1, we can rewrite it as A = 22 - C.

Substitute this value of A into Equation 2:

13(22 - C) + 10C = 277.

Now, distribute and simplify:

286 - 13C + 10C = 277.

Combine like terms:

-3C + 286 = 277.

Subtract 286 from both sides:

-3C = -9.

Divide both sides by -3:

C = 3.

Now, substitute this value of C back into Equation 1:

A + 3 = 22.

Subtract 3 from both sides:

A = 19.

Therefore, there were 19 adults and 3 children who attended the play.