8th grade word problem!!?
Tickets for the school dance that were bought before the dance were $2 each. Tickets bought at the door were $3 each. Altogether 478 tickets were sold and a total of $1110 were made. How many tickets were sold before the dance and how many were sold at the door?
Answers & Comments
Verified answer
Let the no of tickets bought at the door be x
THEN , the no of tickets sold before the dance WILL BE ( 478-x )
Amount collected = 3x + 2 ( 478-x) = 1110
3x + 956 - 2x = 1110
x = 154
ANSWER 154 at the door + 324 before the dance
CHECK
154 X 3 = $ 462
324 X 2 = $ 648
ADD = $ 1110
where x is the number of tickets purchased before the dance and y is the number purchased at the door:
2x + 3y = 1110
x + y = 478
x = 478 - y
2(478 - y) + 3y = 1110
956 - 2y + 3y = 1110
956 + y = 1110
y = 154, so 154 tickets where sold at the door.
478 - 154 = x = 324 tickets sold before.
2N + 3(478 -- N) = 1110 gives N = 3*478 -- 1110 = 324
324 @ $2 and 154 @ $3 ANSWER
x = presold tickets
y = tickets sold at the door
1)...2x + 3y = 1110
2)...x + y = 478
From 2) x = 478 - y
Substitute for x in 1)
1a)...2(478 - y) + 3y = 1110
956 + y =1110
y = 154
x = 478 - 154 = 324
-----------------------------------------