student tickets to the school musical cost $3 each. All other tickets cost $5 each. Suppose that 272 tickets were sold for a total of $1120. How many tickets of each type were sold?
first we represent unknowns with variables.
let x = number of $3-tickets
since the total number of tickets ($3 and $5) is equal to 272,
let 272-x = number of $5-tickets
then we set-up the equation. to get the total cost, we multiply each price of the ticket with their number. thus,
3x + 5(272-x) = 1120
3x + 1360 - 5x = 1120
3x - 5x = 1120 - 1360
-2x = -240
x = 120 (number of $3-tickets)
272-x = 152 (number of $5-tickets)
hope this helps~ :)
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the number of student tickets sold is "s" and the number of all other tickets sold is "o."
According to the given information, student tickets cost $3 each, so the total cost of student tickets sold is 3s.
Similarly, all other tickets cost $5 each, so the total cost of all other tickets sold is 5o.
We also know that the total number of tickets sold is 272, which means:
s + o = 272 (equation 1)
And the total revenue generated from the ticket sales is $1120, which implies:
3s + 5o = 1120 (equation 2)
Now, we have a system of two equations with two unknowns (s and o). We can solve this system to find the values of s and o.
Let's solve this system using the substitution method:
From equation 1, we can express s in terms of o:
s = 272 - o (equation 3)
Substitute equation 3 into equation 2:
3(272 - o) + 5o = 1120
Simplify the equation:
816 - 3o + 5o = 1120
816 + 2o = 1120
2o = 1120 - 816
2o = 304
o = 304/2
o = 152
Substitute the value of o into equation 1 to find s:
s + 152 = 272
s = 272 - 152
s = 120
Therefore, 120 student tickets and 152 all other tickets were sold.