A karate club is having a pancake breakfast to raise money for new gym equipment. The raph shows the amount of money that will be raised for different numbers of tickets sold. The club spent $175 on supplies for the breakfast. If 20 tickets have been sold so far, how many more tickets must be sold to cover the cost of supplies?
Point 1: 10,50
Point 2: 20,100
Point 3: 35,175
Point 4: 50,250
To find the number of tickets that must be sold to cover the cost of supplies, we need to determine the equation of the line that represents the amount of money raised for different numbers of tickets sold.
Let's label the number of tickets sold as x and the amount of money raised as y.
From the given data, we can form two points: (20, 100) and (35, 175).
Using these two points, we can find the equation of the line using the slope-intercept form:
y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
where (x1, y1) = (20, 100) and (x2, y2) = (35, 175).
Plugging in these values:
y - 100 = (175 - 100) / (35 - 20) * (x - 20)
Simplifying:
y - 100 = 75/15 * (x - 20)
y - 100 = 5 * (x - 20)
y - 100 = 5x - 100
y = 5x
Now, let's find the y-value when the number of tickets sold is 20.
y = 5 * 20
y = 100
So far, $100 has been raised from selling 20 tickets.
To cover the cost of supplies, which is $175, we need to subtract the amount raised from the total cost:
175 - 100 = 75
Therefore, we need to sell 75 more tickets to cover the cost of supplies.