Question

PLEASE SHOW WORK

A local group is selling tickets to an event. The event will occur 2 different weekends. The group sold 85 regular tickets and 24 senior citizen tickets the first weekend and made $994. They only sold 45 regular tickets and 12 senior citizen tickets the second weekend and made $522. Find the price of a regular ticket and the price of a senior citizen ticket.

Answer 1

S = 6

R = 10

Explanation:

Givens

Let the Regular Tickets be R

Let the Senior Citizen tickets be S

Equations

85r + 24s = 994 (1)

45r + 12s = 522 (2)

Solution

Multiply equation 2 by 2

• 2(45r + 12s = 522)
• 90r + 24s = 1044 Subtract (1)
• 85r + 24s = 994
• 5r = 50 Divide by 5
• 5r/5 = 50/5 Do the division
• r = 10

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

Solve for s

• 45r + 12s = 522 Substitute r = 10
• 45*10 + 12s= 522 Simplify the left
• 450 + 12s = 522 Subtract 450 from both sides
• 450-450 + 12s = 522-450 Simplify
• 12S= 72 Divide by 12
• 12S/12 = 72 Do the division
• S = 6