Question

A comedy show sells lower level tickets for $77 and upper level tickets for $99. On the opening night 2615 tickets were sold for a total $247071.

Answer 1

Let x represent lower level tickets that cost $77

Let y represent upper level tickets that cost $99

Cost equation: 77x + 99y = 247,071

Tickets equation: x + y = 2615

Using the elimination method, multiply the second equation by -77:

77x + 99y = 247,071

-77x - 77y = -201,355

--> 22y = 45,716

--> y = 2,078

Now plug "y" into either equation and solve for "x". I chose the Tickets equation. x + y = 2615 → x = 2615 - y → x = 2615 - 2078 → x = 537

Answer: lower level = 537 tickets, upper level = 2078 tickets.

Answer 2

Let U = upper

Let L = lower

U + L = 2615

99U + 77L = 247071 You can make your life slightly easier by dividing this equation through by 11

9U + 7L =24461 Multiply the first equation by 7

7U + 7L = 2615 * 7

7U +7L = 18305

====================

Combine the 2 new equations

9U + 7L = 24461

7U + 7L = 18305 Subtract

2U = 6156 Divide by 2

U = 6156 / 2

U = 3078

The Number of Upper Level Tickets sold was 3078