Adult tickets for a play cost $16 and child tickets cost $5. If there were 22 people at a performance and the theater collected $275 from ticket sales, how many children attended the play?

A) 6
B) 7
C) 8
D) 15

adult ticket 30$ child tcket 20$, 19 tickets sold total 460

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that the number of adult tickets sold is A, and the number of child tickets sold is C. We know that the total number of people who attended the play is 22, so we can write the equation:

A + C = 22

We also know that the total amount collected from ticket sales is $275. Since adult tickets cost $16 and child tickets cost $5, we can write another equation:

16A + 5C = 275

Now, we can solve this system of equations. There are several ways to do this, but one common method is substitution. We can rearrange the first equation to solve for A:

A = 22 - C

Then, substitute this expression for A in the second equation:

16(22 - C) + 5C = 275

Now, simplify and solve for C:

352 - 16C + 5C = 275
-11C = -77
C = 7

Therefore, 7 children attended the play.

The answer is option B) 7.

Just substitute the numbers into your equation and see what works. For example, (A)if 6 children are going and there are 22 people, then there must be 16 adults. So, 16(16)+5(6)needs to equal 275. It doesn't, so it is not correct.

(B) 16(15)+5(7) if this equals 275, you have your answer. If that doesn't work you have to go ahead and do the rest. Good Luck!