Q:

Beth bought 20 tickets to a movie, where adult tickets cost $8.00 and senior citizen tickets cost $4.00. She spent a total of $140. Which system of equations will determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased?

Accepted Solution

A:
Answer:The Total number of adults ticket's is 15The Total number of Senior citizen ticket's is 5 Step-by-step explanation:Given as :The total number of movies tickets were bought = 20The cost of adults tickets = $ 8.00The cost of senior citizen tickets = $ 4.00The total money spent on movie tickets = $ 140Let The total number of adults tickets = AAnd The total number of senior citizen tickets = SNow, According to questionThe total number of movies tickets were bought = 20I.e The total number of adults tickets + The total number of senior citizen tickets = 20Or, A + S = 20And $ 8 A + $ 4 S = $ 140  .........1I.e 8 × ( A + S ) = 8 × 20Or, 8 A + 8 S = 160         .......2Solving the equation 1 and 2Or, (  8 A + 8 S ) - (  8 A + 4 S ) = 160 - 140Or, (  8 A - 8 A ) + ( 8 S - 4 S ) = 20or, 0 + 4 S = 20∴ S = [tex]\frac{20}{4}[/tex]I.e S = 5So, The number of Senior citizen ticket's = 5Put The value of S in eq 1So,  8 A +  4 × 5 = 140 Or, 8 A = 140 - 20Or, 8 A = 120∴  A = [tex]\frac{120}{8}[/tex]I.e A = 15So, The number of adult's tickets = 15Hence The Total number of adults ticket's is 15And The Total number of Senior citizen ticket's is 5    Answer