Algebra, Elimination

Question

Tickets to the fair cost $8 for children and $13 for adults. On Thursday 164 people enter the fair and they collected $1762 in ticket sales. How many children and how many adults came?

Answer 1

You are going to set up two equations. The first is the number of children plus the number of adults equals 164.

C + A = 164.

The second is multiplying the amount for each ticket by the type of ticket, adding those together and getting the total amount of money.

8C + 13A = 1762.

Now, since you can't solve an equation with two variables (letters), you need to find a way to get rid of one of the variables. You can do that be rearranging the first equation.

C+A = 164 is the same as C = 164 - A.

Now, in the second equation, instead of C we can use 164 - A.

8(164-A) + 13A = 1752.

Distribute the 8. 1312 - 8A + 13A = 1752

Combine like terms. 1312 + 5A = 1752.

Subtract 1312 from both sides. 5A = 440.

Divide both sides by 5. A = 88.

So there were 88 adults. Just subtract 88 from the total number to get the number of children.

164 - 88 = 76 children.