Question

for a production of sweeney Todd in Las Vegas, orchestra seats cost $42 and mezzanine seats cost $25. if a group of 14 people show up and spend a total of $486, how many of each kind of seat did they buy? use elimination to solve. please help!​

Answer 1

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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