Question 542054: My daughter got the following word problem for homework, but neither of us can recall how to solve this sort of problem:
Ben sold some tickets for a basketball game. Adult tickets were $5 and student tickets were $3. Ben collected $180 for the 50 tickets he sold. How many adult and child tickets did he sell?
If you could point us in the right direction, I would greatly appreciate it!
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Start by letting A = the number of adult tickets and S = the number of student tickets.
The adult tickets cost $5.00 each so the total collected from the adult ticket sales is: $5.00(A) and, similarly, the total amount collected from the student ticket sales is $3.00(S) and the sum of these two amounts is given as $180.00
Also, the total number of tickets sold was 50 so A+S = 50.
Now you can write the necessary equations to answer the question posed by the problem.
$5*A+$3*S = $180 and...
A+S = 50 Rewrite this as S = 50-A and substitute into the first equation.
$5*A+$3*(50-A) = $180 Simplify.
5A+150-3A = 180 Combine the A's
2A+150 = 180 Subtract 150 from both sides.
2A = 30 Divide both sides by 2.
A = 15 This is the number of adult tickets sold.
S = 50-A
S = 50-15
S = 35 This is the number of student tickets sold.
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