Mathematics, 17.09.2019 05:00 shacarabrown49

Atheater owner wants to divide a 3600 seat theater into three sections, with tickets costing $60, $90, and $100, depending on the section. he wants to have twice as many $ 60 tickets as the sum of the other tickets, and he wants to earn $256,000 from a full house. find how many seats he should have in each section.

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Answer from: kebo63

2400 in the section of cost $60 for each ticket

800 in the section of cost $90 for each ticket

400 in the section of cost $100 for each ticket

Step-by-step explanation:-

- A theater owner wants to divide a 3600 seat theater into 3 sections

- The tickets of the sections costing $60, $90, and $100

- He wants to have twice as many $ 60 tickets as the sum of the

other tickets

- He wants to earn $256,000 from a full theater

- Assume that x represents the number of tickets cost $60, y represents

the number of tickets cost $90, and z represents the number of tickets

cost $100

∵ The total number of tickets = 3600

∴ x + y + z = 3600 ⇒ (1)

∵ The number of $60 tickets is twice the sum of the other tickets

∴ x = 2(y + z)

- divide both sides by 2

∴ $\frac{x}{2}=y+z$ ⇒ (2)

- Substitute equation (2) in equation (1)

∴ $x+\frac{x}{2}=3600$

∴ 1.5x = 3600

- Divide both sides by 1.5

∴ x = 2400

∵ He wants to earn $256,000 from a full theater

∵ x cost $60 each

∵ y cost $90 each

∵ z cost $100 each

∴ 60x + 90y + 100z = 256000

∴ 60(2400) + 90y + 100z = 256000

∴ 144000 +90y + 100z = 256000

- Subtract both sides by 144000

∴ 90y + 100z = 112000

- Divide both sides by 10 to simplify it

∴ 9y + 10z = 11200 ⇒ (3)

- Substitute value of x in equation (2)

∴ $\frac{2400}{2}=y+z$

∴ 1200 = y + z

∴ y + z = 1200 ⇒ (4)

- Solve equations (3) , (4) to find y and z

- Multiply equation (4) by -10 to eliminate z

∴ -10y - 10z = -12000 ⇒ (5)

- Add equations (3) and (5)

∴ -y = -800

- Multiply both sides by -1

∴ y = 800

- Substitute the value of y in equation (4) to find z

∴ 800 + z = 1200

- subtract both sides by 800

∴ z = 400

∴ The number of seats in each section:

2400 in the section of cost $60 for each ticket

800 in the section of cost $90 for each ticket

400 in the section of cost $100 for each ticket

Answer from: Quest

if im undersanding the question correctly, its organized from 10

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

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