Physics, 09.02.2023 08:10 tylerineedhelp

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?

Answers

Answer from: lolz55678

General admission:784

Reserved seats:349

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

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)

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

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

Answer from: Quest

where are the vectors ?

Answer from: Quest

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.

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Admission to a baseball game is $2.00 for general admission and $6.50 for reserved seats. The receip...