They buy 8 orchestra seats and 6 mezzanine seats
Step-by-step explanation:
For a production of Sweeney Todd in Las Vegas
- Orchestra seats cost $42
- Mezzanine seats cost $25
- A group of 14 people show up and spend a total of $486
We need to find how many of each kind of seat they bought
Assume that the group of people takes x orchestra seats and y mezzanine seats
∵ The group of 14 people show up
∵ x represents the number of orchestra seats
∵ y represents the number of mezzanine seats
∴ x + y = 14 ⇒ (1)
∵ Orchestra seats cost $42 each
∵ Mezzanine seats cost $25 each
∵ The group of people spend a total of $486
∴ 42 x + 25 y = 486 ⇒ (2)
Now we have system of equations to solve it
Multiply equation (1) by -25 to eliminate y
∵ -25 x - 25 y = -350 ⇒ (3)
- Add equations (2) and (3)
∴ 17 x = 136
- Divide both sides by 17
∴ x = 8
Substitute the value of x in equation (1) to find y
∵ 8 + y = 14
- Subtract 8 from both sides
∴ y = 6
They buy 8 orchestra seats and 6 mezzanine seats
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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