A family of twelve spent $266 on circus tickets, with adult tickets costing $23 and children's tickets $21. How many adults attended?

To determine the correct number of adults who attended the circus, we can set up a system of equations based on the information provided. Let ( a ) represent the number of adults and ( c ) represent the number of children.

We know from the problem that:

1. The total number of family members (adults and children) is 12.

[

a + c = 12

]

2. The total amount spent on tickets is $266, with adult tickets costing $23 each and children's tickets costing $21 each.

[

23a + 21c = 266

]

We can solve this system step by step. First, we can express ( c ) in terms of ( a ) from the first equation:

[

c = 12 - a

]

Next, we substitute this expression for ( c ) into the second equation:

[

23a + 21(12 - a) = 266

]

Expanding this gives:

[

23a + 252 - 21a = 266

]

Combining like terms results in:

[

2a + 252 = 266

]

Now