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koban [17]
3 years ago
15

You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 per performance. A sold-out p

erformance brings you $3125. Let x represent the number of​ sold-out performances. How many sold-out performances must be played in order for you to break even?
Mathematics
1 answer:
Alchen [17]3 years ago
8 0

Answer: 48 sold-out performances must be played in order for you to break even.

Step-by-step explanation:

Let x represent the number of sold-out performances must be played in order for you to break even.

You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 per performance. This means that the total cost of x sold out performances would be

2500x + 30000

A sold-out performance brings you $3125. This means that he total revenue from x sold out performances would be

3125x

To break even, cost = revenue

Therefore,

2500x + 30000 = 3125x

3125x - 2500x = 30000

625x = 30000

x = 30000/625

x = 48

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The company bought 9 computers and 6 printers

<em><u>Solution:</u></em>

Let "x" be the number of computers bought

Let "y" be the number of printers bought

cost of 1 computer = $ 585

cost of 1 printer = $ 385

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Therefore, we can frame a equation as:

number of computers bought + number of printers bought = 15

x + y = 15 ------ eqn 1

<em><u>The company spends $7,575</u></em>

Therefore, we can frame a equation as:

number of computers bought x cost of 1 computer + number of printers bought x cost of 1 printer = 7575

x \times 585 + y \times 385 = 7575

585x + 385y = 7575 ------ eqn 1

<em><u>Let us solve eqn 1 and eqn 2</u></em>

From eqn 1,

x = 15 - y --------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

585(15 - y) + 385y = 7575

8775 - 585y + 385y = 7575

-200y = 7575 - 8775

-200y = -1200

y = 6

<em><u>Substitute y = 6 in eqn 3</u></em>

x = 15 - 6

x = 9

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