# algebra

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Adult tickets for a play cost \$13 and child tickets cost \$3. If there were 20 people at a performance and the theater collected \$200 from ticket sales, how many children attended the play?

• algebra -

Set up a system of equations to model the situation.

Let a be the number of adult tickets sold, and let c be the number of child tickets sold.

See what you get, and I'll help you.

• algebra -

a+c=20??

• algebra -

That's one of your equations, but a system of equations is two equations.

Find the other using the ticket pricing.

• algebra -

13a+3c=200??

• algebra -

Yes, very good. Now, we are trying to find the number of children who attended the play (c).

We have these equations:

a + c = 20
13a + 3c = 200

The easiest way to solve this is substitution. Solve the first equation for a, and then plug that into the second equation. You will then have all c's in the equation and will be able to solve it like any other equation.

• algebra -

a=20-c
13(20-c)+3c = 200
260 -13c +3c = 200
60=10c
6=c

• algebra -

The jurassic zoo charges \$14 for each adult admission and \$10 for each child . The total bill for the 100 people from a school trip was \$1,0. How many adults and how many children went to the zoo?

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