Question

the theaters sell tickets for a concert. tickets for the lower level are $35 each and tickets for the upper level are $25 each. the theater sold 350 tickets for $10,250. how many tickets were sold in each section

Answer 1

Equation 1 for tickets sold:
$35x + $25y = $10,250

Equation 2 for quantity (number #) of tickets sold:
x + y = 350

Use substitution method:

y = 350 - x

35x + 25 (350 - x) = $10,250

35x + $8750 - 25x = $10,250

10x + $8750 = $10,250
- $8,750 -$8,750

10x = 1,500

x = 150

y = 350 - 150

y = 200

Check the answers:

$35 (150) + $25 (200) =

$5,250 + $5,000 = $10,250

Answer 2

9514 1404 393

Answer:

• 150 lower level
• 200 upper level

Explanation:

Let x represent the number of lower-level tickets sold. Then the total revenue is ...

35x +25(350-x) = 10250

10x +8750 = 10250 . . . simplify

10x = 1500 . . . . . . . . . subtract 8750

x = 150 . . . . . . . . . . . lower-level tickets sold

350-x = 200 . . . . . upper level tickets sold

There were 150 tickets sold for the lower level, and 200 sold for the upper level.