SOLUTION: Tickets for a train ride were $120 for a sleeping room, $80 dollars for a berth, and $50 for a coach seat. The total ticket sales were $8600. If there were 20 more berth tickets th

Question 145297: Tickets for a train ride were $120 for a sleeping room, $80 dollars for a berth, and $50 for a coach seat. The total ticket sales were $8600. If there were 20 more berth tickets than sleeping room tickets and 3 times as many coach tickets as sleeping room tickets, how many of each type of ticket were sold?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = no. of rooms
Let y = no. of berths
Let z = no. of seats
:
Write an equation for each statement:
:
"Tickets for a train ride were $120 for a sleeping room, $80 dollars for a berth, and $50 for a coach seat. The total ticket sales were $8600."
120x + 80y + 50z = 8600
:
"there were 20 more berth tickets than sleeping room tickets"
y = x + 20
:
" 3 times as many coach tickets as sleeping room tickets,"
z = 3x
:
how many of each type of ticket were sold?
:
Substitute (x+20) for y and 3x for z in the 1st equation:
120x + 80(x+20) + 50(3x) = 8600
:
120x + 80x + 1600 + 150x = 8600; multiplied whats in the brackets
:
120x + 80x + 150x = 8600 - 1600; subtracted 1600 from both sides
:
350x = 7000
x =
x = 20 sleeping room tickets
:
I'll let you find y and z using the 2nd and 3rd equations
:
Check your solutions in the $total equation
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