Tickets for a school event were $2.50 for students and $3.50 for parents. If a total of 80 tickets were sold for $234.00, how many students and parent tickets were sold?
st = Number of students
pr = Number of parents
pr = 80 - st
2.5 * st + 3.5 * pr = 234
2.5 * st + 3.5 * ( 80 - st ) = 234
2.5 st + 3.5 * 80 - 3.5 St = 234
2.5 st + 280 - 3.5 st = 234
280 - st = 234 Add st to both sides
280 - st + st = 234 + st
280 = 234 + st Subtract 234 to both sides
280 - 234 = 234 + st - 234
46 = st
st = 46
pr = 80 - 46 = 34
46 students and 34 parents
Proof :
2.5 $ * 46 + 3.5 $ * 34 = 115 $ + 119 $ = 234 $
To solve this problem, we can use a system of equations. Let's represent the number of student tickets as 's' and the number of parent tickets as 'p'.
We know that the price of a student ticket is $2.50 and the price of a parent ticket is $3.50. We also know that a total of 80 tickets were sold for $234.00.
From this information, we can create two equations:
1. The total number of tickets sold is 80:
s + p = 80
2. The total amount of money collected from ticket sales is $234.00:
2.50s + 3.50p = 234
Now we can solve this system of equations. One way to solve it is by substitution.
From the first equation, we can express s in terms of p by subtracting p from both sides: s = 80 - p.
Substituting this expression for s into the second equation, we get: 2.50(80 - p) + 3.50p = 234.
Now we can solve for p. Simplifying the equation, we have: 200 - 2.50p + 3.50p = 234.
Combining like terms, we get: 200 + p = 234.
Subtracting 200 from both sides, we find that p = 34.
Now we can substitute this value of p back into the first equation to find s:
s + 34 = 80
s = 80 - 34
s = 46.
Therefore, 46 student tickets and 34 parent tickets were sold.