Question 1094912: A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3235 tickets overall. It has sold 182 more $20 tickets than $10 tickets. The total sales are $62,170. How many tickets of each kind have been sold?
How many %10 dollar tickets were sold?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30.
The team has sold 3235 tickets overall. It has sold 182 more $20 tickets than $10 tickets.
The total sales are $62,170. How many tickets of each kind have been sold?
How many $10 dollar tickets were sold?
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Let T be the number of $10-tickets sold.
Then the number of $20-tickets is (T+182), according to the condition,
and the number of $30-tickets is (3235 - T - (T+182)) = 3053-2T.
Hence, your "money equation" is
10T + 20*(T+182) + 30*(3053-2T) = 62170.
Simplify and solve for T:
(10T + 20T - 60T) = 62170 - 20*182 - 30*3053,
-30T = -33060 =====> T =  = 1102.
Thus, 1102 of the $10-tickets, 1102 + 182 = 1284 of the $20-tickets and 3235-1102- 1284 = 849 of the $30-tickets were sold.
Check. $10*1102 + $20*1284 + $30*849 = 62170. ! Correct !
Lesson to learn from this solution
This problem is for one unknown, not for three.
Your major task, when you start solve it, is to select the key unknown,
and then to express other quantities via that unknown.
Then write the basic governing equation and solve it accurately.
The way @josgarithmetic tries to teach you is NOT THE WAY for solving such problems.
It is the way to NOWHERE.
To see more similar solved problems, look into the lesson
- More solved word problems on a single linear equation
in this site.
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Dear tutor @greenestamps !
This problem is designed and assigned to 6-th or 7-th grade students, who did not study yet systems of equations and
DEFINITELY did not study systems of equations in three unknowns.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Tutor ikleyn posts some very good responses to questions; however, she is highly prejudiced about the "right" way to work problems. The method suggested by josgarithmetic is NOT, as ikleyn says, a road to nowhere.
In fact, if you are solving the problem using matrices to solve a system of linear equations, the method suggested by josgarithmetic is exactly the way to go.
On the other hand, if you are solving the problem using algebra with pencil and paper, I would definitely go with the one-variable method shown by ikleyn.
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