Quinn is selling raffle tickets. The Ultra tickets cost $3 and the deluxe tickets cost $2. Quinn sold 89 tickets for $235. How many of each ticket did Quinn sell?
Let x = number of ultra tickets and y = number of deluxe tickets
x + y = 89
3x + 2y = 235
-> -3(x + y = 89)
= -3x + -3y = -267
-3x + -3y = -267
+ 3x + 2y = 235
____________________
-y = -32
y = 32
x + y = 89
x + 32 = 89
x = 57
Quinn sold 57 Ultra tickets and 32 deluxe tickets.
U+D=89
3U+2D=235
D=89-U
3U+2(89-U)=235
solve for U first.
To solve this problem, we can set up a system of equations based on the given information.
Let's define the variables:
- Let's say x represents the number of Ultra tickets sold.
- Let's say y represents the number of Deluxe tickets sold.
Now, we can set up two equations based on the given information:
Equation 1: The total number of tickets sold is 89: x + y = 89
Equation 2: The total amount collected from ticket sales is $235: 3x + 2y = 235
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the substitution method:
From Equation 1, we can express x in terms of y by subtracting y from both sides of the equation: x = 89 - y
Now, substitute this expression for x in Equation 2:
3(89 - y) + 2y = 235
267 - 3y + 2y = 235
267 - y = 235
-y = 235 - 267
-y = -32
Dividing both sides of the equation by -1, we get:
y = 32
Now, substitute this value of y in Equation 1 to find x:
x + 32 = 89
x = 89 - 32
x = 57
Therefore, Quinn sold 57 Ultra tickets and 32 Deluxe tickets.