Question

question 14 of 15, step 1 of 1
admission to a baseball game is $2.00 for general admission and $6.00 for reserved seats. the receipts were $3798.00 for 1297 paid admissions. how many of each ticket were sold? (round to nearest integer if necessary.)
answer
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____ general admission tickets sold
____ reserved seating tickets sold

Explanation:

Step1: Define variables

Let $x$ = number of general admission tickets, $y$ = number of reserved seats tickets.

Step2: Set up total tickets equation

Total paid admissions: $x + y = 1297$

Step3: Set up total receipts equation

Total revenue: $2x + 6y = 3798$

Step4: Solve for $x$ from Step2

$x = 1297 - y$

Step5: Substitute $x$ into Step3 equation

$2(1297 - y) + 6y = 3798$
Expand: $2594 - 2y + 6y = 3798$
Simplify: $2594 + 4y = 3798$

Step6: Solve for $y$

$4y = 3798 - 2594$
$4y = 1204$
$y = \frac{1204}{4} = 301$

Step7: Solve for $x$

$x = 1297 - 301 = 996$

Answer:

996 general admission tickets sold
301 reserved seating tickets sold