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Math  /  Algebra

QuestionQuestion 6 of 25 After the drama club sold 100 tickets to a show, it had $300\$ 300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700\$ 700 profit. Which equation models the total profit, yy, based on the number of tickets sold, xx ? A. y+300=4(x+100)y+300=4(x+100) B. y−300=4(x−100)y-300=4(x-100) C. y−300=2.5(x−100)y-300=2.5(x-100) D. y+300=2.5(x+100)y+300=2.5(x+100) SUBMIT

Studdy Solution

STEP 1

1. The drama club's profit is based on the number of tickets sold.
2. After selling 100 tickets, the profit was 300.<br/>3.Afterselling200tickets,theprofitincreasedto300.<br />3. After selling 200 tickets, the profit increased to 700.
4. We need to find an equation that models the total profit y y based on the number of tickets sold x x .

STEP 2

1. Determine the change in profit and the change in tickets sold.
2. Calculate the rate of profit per ticket.
3. Use the rate to write an equation in point-slope form.
4. Match the equation to one of the given options.

STEP 3

Determine the change in profit and the change in tickets sold.
Change in profit: 700−300=400 700 - 300 = 400 Change in tickets: 200−100=100 200 - 100 = 100

STEP 4

Calculate the rate of profit per ticket.
Rate of profit per ticket is the change in profit divided by the change in tickets:
Rate=400100=4 \text{Rate} = \frac{400}{100} = 4

STEP 5

Use the rate to write an equation in point-slope form. We use the point (100, 300) for this purpose.
Point-slope form: y−y1=m(x−x1) y - y_1 = m(x - x_1)
Substitute y1=300 y_1 = 300 , m=4 m = 4 , and x1=100 x_1 = 100 :
y−300=4(x−100) y - 300 = 4(x - 100)

STEP 6

Match the equation to one of the given options.
The equation y−300=4(x−100) y - 300 = 4(x - 100) matches option B.
The correct answer is: **B. y−300=4(x−100) y - 300 = 4(x - 100) **

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