How do I figure out this question?

Question

483 theater seats. Tickets for adults are $56 and $27 for children. If i make $18,580 for sold out theater how man of each type ticket did i sell?

Answer 1

483 theater seats. Tickets for adults are $56 and $27 for children. If I make $18,580 for a sold-out theater, how many of each ticket type did I sell? This problem can be solved using a system of two linear equations. Begin by re-reading the problem and underlining anything that represents a total as follows: 483 theater seats. Tickets for adults are $56 and $27 for children. If I make $18,580 for a sold-out theater, how many of each ticket type did I sell?

Now, I always think of given totals to help with this process because equations are statements of equality and you need to write out two linear equations using what's given. I know that one of my equations will be a variable expression equal to 483, the total number of theater seats filled; and the other equation will be a variable expression equal to $18,580, the total amount of money made from a sold out theater. Okay! Next, let's think about what our variables are in the two equations. The amount of adult tickets sold plus the amount of children's tickets sold in this scenario will give us 483, keeping in mind that we have a sold-out theater. Also, the amount of adult tickets sold multiplied by $56 plus the amount of children's tickets sold multiplied by $27 will give us the total amount made for the sold-out theater or $18,580. Notice that the variables in this problem are the number of adult and children's tickets sold; hence, the exact two things we're asked to find. Alright! Now, let's assign our variables a letter so that we can write out our system of equations.

Let a = the number of adult tickets sold

Let c = the number of children's tickets sold

Using what we discussed earlier, let's write out our two equations: The amount of adult tickets sold plus the amount of children's tickets sold in this scenario will give us 483, keeping in mind that we have a sold-out theater. Also, the amount of adult tickets sold multiplied by $56 plus the amount of children's tickets sold multiplied by $27 will give us the total amount made for the sold-out theater or $18,580. Therefore, a + c = 483 and 56a+27c = 18,580.

Now that we have our two equations, let's re-write them in the form of a system and then solve (using your method of choice).

Elimination Method:

56a+27c = 18,580

27 ( a + c = 483 )

↓ ↓ ↓

56a+27c = 18,580

– ( 27a+27c = 13,041)

↓ ↓ ↓

56a+27c = 18,580

– 27a–27c = –13,041

29a + 0 = 5539

↓ ↓ ↓

29a = 5539

a = 191 Plug a into one of your original equations to solve for c.

↓ ↓ ↓ .

191 + c = 483

–191 –191

c = 292

Therefore, you sold 191 adult tickets and 292 children's tickets. Done!