Ticket sale for a music concert was $2,160. Three times as many tickets were sold for the Saturday night concert as were sold for the Sunday afternoon concert. Two times as many tickets were sold for the Friday night concert as were sold for the Sunday afternoon concert. Tickets for all three concerts sold for $2.00 each. Find the number of tickets sold for the Saturday night concert.
Sun: X tickets were sold.
Sat: 3x " " "
Fri: 2x " " "
$2(x + 3x + 2x) = $2160.
X = ?
6x=1080
X=180
To find the number of tickets sold for the Saturday night concert, we can solve this problem step by step.
Let's start by assigning variables to the unknown quantities. Let S, F, and A represent the number of tickets sold for the Saturday night, Friday night, and Sunday afternoon concerts, respectively.
Given that the total ticket sale was $2,160 and tickets for all three concerts sold for $2 each, we can set up an equation:
2S + 2F + 2A = 2,160
Now, we're given some additional information:
- Three times as many tickets were sold for the Saturday night concert as were sold for the Sunday afternoon concert:
S = 3A
- Two times as many tickets were sold for the Friday night concert as were sold for the Sunday afternoon concert:
F = 2A
Substitute the values of S and F into the equation:
2(3A) + 2(2A) + 2A = 2,160
Simplify the equation:
6A + 4A + 2A = 2,160
12A = 2,160
To find the value of A (the number of tickets sold for the Sunday afternoon concert), divide both sides of the equation by 12:
A = 2,160 / 12
A = 180
Now that we know A, we can find the number of tickets sold for the Saturday night concert by substituting A back into the equation:
S = 3A
S = 3 * 180
S = 540
Therefore, the number of tickets sold for the Saturday night concert is 540.