Question

Admission to a baseball game is $2.00 for general admission and $6.50 for reserved seats. The receipts were $3836.50 for 1133 paid admissions. How many of each ticket were sold?

Answer 1

General admission:784

Reserved seats:349

Step-by-step explanation

Step 1

set the equations

let x represents the number of general admisions tickets sold

let y represents the number of greserved seats tickets sold

price of general admission: $ 2.0

price of reserved seat: $ 6.5

so

a)The receipts were $3836.50,hence

`2x+6.5y=3836.5\Rightarrow equation(1)`

B) also, the number of tickets sold is 1133, so

`x+y=1133\Rightarrow equation(2)`

Step 2

solve the equations

`\begin{gathered} 2x+6.5y=3836.5\Rightarrow equation(1) \\ x+y=1133\Rightarrow equation(2) \end{gathered}`

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

`\begin{gathered} x+y=1133\Rightarrow equation(2) \\ \text{subtract y in both sides} \\ x+y-y=1133-y \\ x=1133-y \end{gathered}`

now, replace in equation(1)

`\begin{gathered} 2x+6.5y=3836.5\Rightarrow equation(1) \\ 2(1133-y)+6.5y=3836.5\Rightarrow equation(1) \\ \text{break the parenthesis} \\ 2266-2y+6.5y=3836.5 \\ \text{add like terms} \\ 2266+4.5y=3836.5 \\ \text{subtract 266 in both sides} \\ 2266+4.5y-2266=3836.5-2266 \\ 4.5y=1570.5 \\ \text{divide both sides by 4.5} \\ (4.5y)/(4.5)=(1570.5)/(4.5) \\ y=349 \end{gathered}`

hence

the number of reserved seats sold is 349

b)now, replace the y value in equation (2) to find x

`\begin{gathered} x+y=1133\Rightarrow equation(2) \\ x+349=1133 \\ \text{subtract 349 in both sides} \\ x+349-349=1133-349 \\ x=784 \end{gathered}`

hence

the number of general admission tickets sold is 784

I hope this helps you