Question

Tickets for the community fair cost $12 for adults and $5 dollars for children. On the first day of the fair, 322 tickets were sold for a total of $2,254. How many adult tickets and how many child tickets were sold?

Answer 1

92 adult tickets were sold

230 child tickets were sold

Step-by-step explanation

Step 1

set the equations

let x represents the number of adult tickets sold

let y represents the number of child tickets sold

cost of adult ticket: 12

cost for child ticket : 5

so

a)On the first day of the fair, 322 tickets were sold

so

`x+y=322\rightarrow equation(1)`

b)total of $2,254

`12x+5y=2254\rightarrow equation(2)`

Step 2

Solve the equations:

`\begin{gathered} x+y=322\rightarrow equation(1) \\ 12x+5y=2254\rightarrow equation(2) \end{gathered}`

a) isolate x in equation (1) and then replace in eqaution(2)

`\begin{gathered} x+y=322\rightarrow equation(1) \\ x=322-y \end{gathered}`

replace in equation (2)

`\begin{gathered} 12x+5y=2254\rightarrow equation(2) \\ 12(322-y)+5y=2254 \\ 3864-12y+5y=2254 \\ \text{add like terms} \\ 3864-7y=2254 \\ 3864-2254=7y \\ 1610=7y \\ \text{divide both sides by 7} \\ (1610)/(7)=(7y)/(t) \\ 230=y \end{gathered}`

b) now, replace the y value in equation (1) and solve for x

`\begin{gathered} x+y=322\rightarrow equation(1) \\ x+230=322\rightarrow equation(1) \\ x=322-230 \\ x=92 \end{gathered}`

therefore

92 adult tickets were sold

230 child tickets were sold

I hope this helps you