Admission to a movie theater is $10 for children and $11 for adults. On a certain day, 43 people bought tickets at the theater and $452 was collected. How many children's tickets were sold and how many adult's tickets were sold?

21 children's tickets were sold and 22 adult's tickets were sold

Step-by-step explanation:

Create a system of equations where c is the number of children's tickets sold and a is the number of adult's tickets sold:

10c + 11a = 452

c + a = 43

Solve by elimination by multiplying the bottom equation by -10:

10c + 11a = 452

-10c - 10a = -430

Add them together and solve for a:

-a = -22

a = 22

So, 22 adult's tickets were sold. Plug this into one of the equations and solve for c:

c + a = 43

c + 22 = 43

c = 21

So, 21 children's tickets were sold and 22 adult's tickets were sold

I'm no expert in this topic, but is it called a "paragraph proof"?