20 more adults than children. Adult tickets were $8, child tickets were $3. The total was $1260, how many adult tickets were bought?

Question

The Little Theater group put on a play. There were 20 more adults attending than children. The adult tickets were $8 each and the child tickets were $3 each. If they collected $1260, how many adult tickets were purchased?

Answer 1

What we have here are a pair of linear equations that we need to draw out. Let's make our variables a for adults and c for children. Now let's put down what we know:

a = c + 20 (20 more adults than children)

8a + 3c = 1260 (total cost of tickets bought is 1260)

 

Since we have a value for a, let's put that into our equation:

8(c + 20) + 3c = 1260

8c + 160 + 3c = 1260

11c + 160 = 1260

 

Now we isolate c:

11c = 1100

c = 100

 

Now we go back to solve for a:

a = 20 + 100

a = 120

 

So 120 adult tickets were bought.