The box office sold 360 tickets to a concert at
the college. The total receipts were $4,170. General
admission tickets cost $15 and student tickets cost $10.
How many of each kind of ticket was sold?
This is what I was doing
x+y=360
x=360-y
10(x)+8(y)=4170?
plugged in 10(360 - y)+8y=4170
Should I have 3600-10y if distribute right?
your 3rd equation is incorrect
general admission is $15
okay. I just realized that. I was doing this late at night and completely missed it. But I got the right solution now.
10(360-y)+15=4170.
-10y+15y+3600=4170. Simply the variable...
..5y+3600=4170. Subtract 3600 from both sides..
Divide the answer by 5.. You should have (y=114)?
To solve this problem, you correctly set up the system of equations:
x + y = 360 (equation 1)
10x + 15y = 4170 (equation 2)
However, there seems to be a mistake in the coefficients of the equation. The cost of general admission tickets is $15, not $10. Therefore, you should have:
10x + 15y = 4170 (equation 2)
By distributing correctly, the equation becomes:
10(360 - y) + 15y = 4170
Now, let's solve the system of equations using the substitution method.
First, express one of the variables in terms of the other from equation 1:
x = 360 - y
Substitute this value of x into equation 2:
10(360 - y) + 15y = 4170
Expand the equation:
3600 - 10y + 15y = 4170
Combine like terms:
5y = 570
Divide both sides by 5:
y = 114
Now, substitute this value of y back into equation 1 to solve for x:
x + 114 = 360
x = 360 - 114
x = 246
Therefore, 246 general admission tickets and 114 student tickets were sold.