You and your friend are selling raffle tickets for a new laptop. You sell 14 more tickets than your friend sells. Together, you and your friend sell 58 tickets. a. Write a system of linear equations that represents this situation. Let xx represent the number of tickets you sell and yy represent the number of tickets your friend sells. System of equations: Question 2 b. How many tickets does each of you sell? You sell tickets. Your friend sells tickets.
Answer: (a)x + y = 58 and x = y + 14 (b) You sold 36 and your friend sold 22.
Tickets that you sold = x Tickets that your friend sold = y
Together, the two of you sold 58 tickets. x + y = 58
You sold 14 more than your friend x = y + 14
So the two equations are: x + y = 58 x = y + 14
------------------------------------------------------------------------ Construct system of equations and solve for x and y ------------------------------------------------------------------------ x + y = 58 ------------ (1) x = y + 14 -------------(2)
Substitute equation (2) into equation (1) (y + 14) + y = 58 y + 14 + y = 58 2y + 14 = 58 2y = 58 - 14 2y = 44 y = 22 ---------------- Substitute into equation (2)
x = y + 14 x = 22 + 14 x = 36
------------------------------------------------------------------------ Find the tickets you and your friend sold ------------------------------------------------------------------------ you = x = 36 your friend = y = 22
------------------------------------------------------------------------ Answer: (a) x + y = 58 and x = y + 14 (b) You sold 36 and your friend sold 22. ------------------------------------------------------------------------
