There were 315 student tickets sold in the opening night
Step-by-step explanation:
The given is:
1. The cost of student ticket is $8
2. The cost of non-student ticket is $10
3. The receipts for opening night came to $3,270 from selling
390 tickets
We need to find how many student tickets were sold
Assume that there were x student tickets and y non-student tickets sold
∵ There were x student tickets and y non-student tickets sold
∵ The number of tickets were sold is 390 tickets
∴ x + y = 390 ⇒ (1)
∵ The cost of each student ticket = $8
∵ The cost of each non-student ticket = $10
∵ They earned $3270 from selling the tickets
∴ 8 x + 10 y = 3270 ⇒ (2)
Now we have system of equations let us solve them
∵ x + y = 390 ⇒ (1)
∴ 8 x + 10 y = 3270 ⇒ (2)
- Multiply equation (1) by -8 to eliminate x
∴ -8 x - 8 y = -3120 ⇒ (3)
- Add equations (2) and (3)
∴ 2 y = 150
- Divide both sides by 2
∴ y = 75
Substitute the value of y in equation(1) to find x
∵ x + y = 390 ⇒ (1)
∴ x + 75 = 390
- Subtract 75 from both sides
∴ x = 315
∵ x represents the number of the student tickets
∴ The number of the student tickets is 315 tickets
There were 315 student tickets sold in the opening night
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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